And the caregiver is his girlfriend? She throws the caregiver out. She insists on driving home. (she is home) for a while, one could go along and find a way to distract her and/or snap her out of it. Now it is almost 24/7 and she has several meltdowns a day. We are in the process of switching out pictures for an earlier time to help her feel at home, but the situation gets worse and escalates multiple times a day. We are trying meds, so far, they just make it worse. My brother drives her around to 'go home' (after she packs all her clothes)(really) and she cries and screams out him for cheating on her the whole time. A few months ago it was my younger brother Jack who was staying with Jack (same person) and his wife without permission. She thought little Jack was about 16 and god knows who Jack and his wife are.
Getting another doctor involved might not be a bad idea, but I don't hold out a lot of hope.
Perhaps moving her environment back in time, and soothing her, and going along with her, and never arguing with her, and the simple passage of time to a different dementia phase will help. Saying, "Oh, I really wish I could take you home now, but the entire block has been evacuated because a broken main. We'll have to make the most of it here for a while. Let's have some ice cream." or "I would never, ever cheat on you. I love you and respect you. I am very sorry something happened to make you think otherwise." or "Dad loved you very much and respected you. He and I talked once and I know he didn't cheat on you." No arguments about "you are home" or "I am your son, not your husband."
This is distressing for all concerned. I hope you and your brother each have the encouragement of a local caregivers support group. If necessary consider counseling for yourselves, to help you understand this. I doubt counseling will help Mom, but possible some drug will be somewhat helpful.
This may be the straw that breaks the camel's back. It may be necessary to consider care center placement for her. That will not stop the behavior. (My friend's father was in assisted living when he was "governor".) But it spreads the burden of dealing with this onto additional shoulders. Of course she will still be your Mom and it will still be a factor in your relationships.
If you do fine anything that helps, any partial solutions to this, please share. It is a topic many people confront, and we learn from each other.
Many care centers that don't accept Medicaid for new residents will after a certain period of private-pay. Don't totally discount the possibility of affording good care. I am not urging you to place your mother, just to be open to all options as her dementia progresses.
And about cost, the reason Medicaid and other programs don't provide 24/7 care in the home is that it is more expensive to do so that to use a care center when the need is at that level. Be certain you are including all the costs -- food, taxes, home maintenance, as well as caregivers, when comparing the costs of keeping Mom at home to using a care center.