Dad's estate, any advice?

Good Lord, what disgustingly greedy people they are. So sorry they are your relatives. Calling them vultures would insult the vultures.

I'm not an estate expert but not sure if the estate has to go through a legal process first? Legal eagles on this site will give you good guidance and others who have dealt with "those" kind of siblings will also give you great advice and perspective. Sorry for you loss. Wishing you peace and resolution.

Is the sister you are in charge with problematic, or are there two sisters, one who didn't even care to come there and now wants it all sold asap, and one who is "good sister" there for you?
If the answer is that you are executor Trust along with a sister you cannot get along with--then you are in for a WORLD of hurt. It is in my humble opinion ALWAYS a mistake to have two in charge. That doesn't work.
When there are this many inheritors the laws of most states allows the sale on the demand of any one of them, but NOT before the estate is settled. You would be well advised to put most of this now in the hands of a lawyer. That will unfortunately eat up approximately 10% of the estate. You could do it with the HELP of an attorney as well.
You do, by law, have certain amounts of time to file probate (if needed--often NOT needed with a trust), to notify all inheritors that they will be inheriting, and to settle and distribute the estate. DO WHAT YOU MUST DO ACCORDING TO LAW and find that out from a lawyer. Then do the rest in the time allotted by the law. And tell the brother and sister that you intend to act METICULOUSLY according to the laws of your state.
Hire help. That is paid for by the estate. Tell the sister and brother that the more problematic they become the longer it will take, the more money will disappear to the sleeves of lawyers.
There is one more option. And that is the one I would take. Resign your position as Trustee, leaving it to the other sister. Then be on her like a gnat on sweat.
Wishing you the best. Families are often a nightmare. Sounds like yours is on track for being one.
ps I see, reading down further that there are three of you. And that it is unclear if you are dealing with a Trust or a Will. They are very different and require very different actions. Number one forget about what he said to you verbally. It is under the law non existant and not worth fighting about. Number 2 it is clear there are three of you and the 2 who never gave a darn has one of them co-trustee or co-executor with you. I say again, I would resign as executor or trustee before lawyer eat up this entire estate with the fighting. You and your sister go and you resign making her the sole executor. Then you can hassle HER. She has to do her duty under the law. It will take her a while to settle the estate, but eventually any way you look at it this duplex is being sold. Get ready to move. Save. Do NOT pay rent. That would be what I would do. You must do as you think best but BEFORE YOU DO ANYTHING, buy one hour of time with a lawyer. The estate has to pay for that. Get his advice. Update us if you are able. Wishing you good luck. Take a deep breath. This is a bad time, but it will pass.

Supposing we agree, just for the sake of the point, that your father's will must stand and that you and your sister will carry it out. That takes care of the business side.

Then even so, it is still *beyond* repellant for your brother to attack you in this way less than a full week after your father's passing, when you have been so closely attached to your father - and presumably *his* father - for so long.

I'm revolted. I don't know what to say. Do you have to have any more direct contact with this person for the time being, or can you make him stay away from you?

Is your co-trustee sister on the same page as you?? Forget about the rest of the group. The co-trustees must follow the Trust instrument. If either you or her deviate - either of you may be removed as trustee by the beneficiaries. It is always a good idea to have an attorney help execute the trust, and take care of the estate taxes or settlement of the estate itself first before greedy hands get a hold of anything. Get an attorney to help with the Trust.

If it's a WILL . . you are not Trustees, you are Executors. His estate needs to be PROBATED. It's still best to get an Estate Law attorney on board to settle his estate LEAGALY.

How is Title currently held with the Duplex? That is very important and must be taken care of first to have a succesfull Real Estate transaction. I would never sell a property from a recently deceased owner without investigation of title first. There may be other variables with the estate - be careful.

I'm sorry your going through this. Death is unfortunately complicated - death and taxes! ugh!

" My Dad did have a will. He requested that the property be split in thirds. Orally he told all of us after the will was done and I had moved down here, that he would like me to have this side of the duplex. My sister already owns two homes and he wanted me to be taken care of. Again, unfortunately, nothing in writing."

Why nothing in writing??? I read your previous posts, and it has been a struggle for you, taking early retirement to move down to FL with your disabled husband to take care of this man who promised something he couldn't make happen.

How much would the entire duplex sell for? Approximately what would be your 1/3 of it?

I am executor of my Mom's Will (who died on September 17, 2018) and it will take a year to complete the probate of her will because she had a house and farmland.  The article "An Overview of Florida's Formal Probate Process" does a good job of giving an overview of what documentation you need when you meet with the attorney for the first time.  I have also included a couple of websites for PDFs about the Florida Probate Court for you to look at.  You and your sister, as co-executors, will need to petition for "Formal Administration" of the Will with the Florida Court and will need to follow their rules and regulations. 

Copy and Paste the URLs to your browser:

https://www.floridabar.org/public/consumer/pamphlet026/

https://www.thebalance.com/understanding-florida-s-simplified-probate-process-3504955

https://www.thebalance.com/formal-probate-estate-fl-3504954
According to the article "An Overview of Florida's Formal Probate Process" by Julie Garber,

The State of Florida boasts a streamlined probate process known as "Summary Administration" that may be used by estates with less than $75,000 worth of assets, or estates where decedents have been dead for more than two years. Estates that do not meet these criteria must follow the more time-consuming probate court-supervised process known as "Formal Administration."

Florida imposes a $400 flat fee for each estate that files for a formal probate.

The Florida probate court may require the following documents from those looking to open a formal probate administration:

Petition for Formal Administration. This document must contain the following information:

--All pertinent information about the person filing the petition, including name, address, interest in the estate, and the name and address of the petitioner's probate attorney.
--All pertinent information regarding the decedent, including legal name, last known address, age at the time of death, the last four digits of the Social Security number, place of death, and state and county of domicile.
--All pertinent information about the beneficiaries of the estate, including legal names, addresses, dates of birth of any minors, and the nature of relationships to the decedent.
--The reason for choosing the county where the petition is being filed, for probating the decedent's estate.
--The reason for naming the chosen Personal Representative (executor), and a list of his or her qualifications to serve under Florida law.
--An itemized list detailing the value and nature of the decedent's assets.
--A declaration whether or not an estate will be required to file federal estate tax return, IRS Form 706.
--A declaration if the decedent had a Last Will and Testament, a statement identifying all unrevoked wills, and any amendment to the wills (called "codicils"), that have been presented for probate, e.g: "Last Will and Testament dated July 1, 2015; First codicil dated July 1, 2017."
--A declaration if the decedent did not have a Last Will and Testament.
--A declaration stating that after the exercise of reasonable diligence, the petitioner was unable to locate any Wills or codicils.

Petition to Waive Bond:
If the decedent had a Last Will and Testament, the document will typically request that the bond be waived.

Waiver of Priority, Consent to Appointment and Waiver of Notice and Bond:
the waiver makes it clear that the beneficiary does not protest the decedent’s will, and has no intention to contest it.

Original Death Certificate.

Last Will and Testament must be filed with the probate court.

Once the probate judge has reviewed and approved the Petition for Administration and related documents, he or she will issue the following orders:
--Testate estates. (Decedent has a Will) then the probate judge will sign an Order Admitting Will to Probate and Appointing Personal Representative (Executor) as well as Letters of Administration.

Hope that this information helps.  Good Luck.

Second comment: (I ran out of character space.)

I had to open a separate "Estate Checking Account" which I used to pay ALL of Mom's bills (medical, attorney, etc.) and court fees for probating my Mom's Will.  The attorney had to send requests to the County Assessors asking for evaluations of the value of the property that my Mom owned and listed in the Will.  Only after the evaluations were done, was I able to do anything with the property.  Notices had to be put in local newspapers notifying creditors that Mom had died and that I had been named as Personal Representative and that if anyone had any bills, they needed to send those to the attorney ASAP. 

You and your sister need to have the duplex evaluated prior to the selling of the property, either to each other or to another person.  That way you are making sure that you get fair market price for the property and to avoid "Capital Gains Tax' if you purchase the duplex unit you are living in.  If you sell the duplex, you can either fix up the tiles and fence, or you can sell the property "as is" and allow the new owners to remodel the duplex to their liking.  I would do whichever gets the most money for you and your siblings (since they seem so concerned about money) and/or whichever is the fastest way to sell the duplex.

Do you have a place to live if you sell the duplex?  You could buy the unit of the duplex that you are living in and sell the other side/unit of the duplex (that your brother and sister are staying in).  Your "third" of the inheritance would be taken out of the sell price of the half/unit that you purchase.   And your brother and sister would receive part of their "thirds" from the sell of the other half/unit of the duplex.  So you would be accepting your "third" of the Estate in the form of half of the duplex ( the unit that you are living in).  If your "third" is less than the sell price of the duplex unit,  then you will need to "buy" the remaining portion of the duplex unit from the estate by paying your sister and brother the remaining amount.  {Clear as MUD???}

Example:  My Mom and 3 siblings inherited farmland in the 1970s.  None of the other siblings wanted the farmland. So the Estate had the farmland value assessed and that value was divided by 4.  Mom inherited her 1/4 of the farmland, and then paid 1/4 of the value to each sibling resulting in Mom owning the farmland. (Let's say that the farmland was valued at $100,000.  So Mom paid $25,000 to each sibling--Total of $75,000--for their share of the farmland).

Please do not get in a hurry to sell the duplex, you need to follow the probate regulations and sometimes it can take 6 months or more before any property can be sold.  And when Medicaid gets involved and request reimbursement from the Estate, it can take even longer until the Probate is completed.

Thank you Geaton. I'm shaking so hard right now and can't even think straightly. My Dad did have a will. He requested that the property be split in thirds. Orally he told all of us after the will was done and I had moved down here, that he would like me to have this side of the duplex. My sister already owns two homes and he wanted me to be taken care of. Again, unfortunately, nothing in writing.

Thank you Geaton. I'm shaking so hard right now and can't even think straightly. My Dad did have a will. He requested that the property be split in thirds. Orally he told all of us after the will was done and I had moved down here, that he would like me to have this side of the duplex. My sister already owns two homes and he wanted me to be taken care of. Again, unfortunately, nothing in writing.