My dad had a stroke 5 years ago and his mobility has gone down hill greatly in the last year. He uses a walker but refuses to use a wheelchair. He has fallen several times in his home. My mom is not strong enough to get him upright when this happens so they end up calling 911 or the neighbors. They never tell me about the medical stuff unless he ends up in the hospital. My mom is caring for him but she is having memory issues and I worry about her now also.
Another thing to think about is will your parents be able to budget for Independent Living or Assisted Living. The cost in my area is between $5k to $7k per month. My Dad sold his house and used the equity to help with the cost.
Your Mom may be in agreement to move to a senior facility as she knows she will get the much needed rest that she deserves. And as Ahmijoy had mentioned in her post, the memory loss could be stress related. Your Dad may be too proud to admit that it is time to move. You can tell him that up to 40% of family caregivers die leaving behind the love one they were caring.... that's not fair to him nor to you to lose Mom that way.
Another idea is to bring in a part-time professional caregiver. You could tell Dad that the person is there to help your Mom with things around the house. That way Dad doesn't feel like the caregiver is there to babysit him. Again, the budget. In my area it runs around $30/hour.
Lot to think about. Let us know what happens.
Eventually Dad needed more help then using a cane, so I bought him a rolling walker. He loved it so much you'd think I had bought him a Mustang :) Yet my Mom didn't want Dad going outside to get the mail with his walker, again with don't want the neighbors to think they were helpless. After Dad fell backwards on the driveway, a neighbor had to help him into the house, after calling 911 and Dad staying overnight in the hospital, Mom gave in with Dad using the walker out in public.
Dad knew it was time to move to senior living, and Independent Living would be a great choice, but Mom refused. She said "maybe in a few years". Guess I would have had to wait until they were 100 years old.
My Mom also refused caregivers and cleaning crews. Sadly a serious head trauma was Mom downfall. After she went into long-term-care, Dad had me call the caregiving agency to help him around the house. After Mom passed he moved to Independent Living, and after that into Assisted Living/Memory Care.
Thus, many of us here had to wait until there was a medical emergency, hospital stay, rehab stay, then into Assisted Living or whatever before we could convince our parents they need to be in a safer environment.
Have a respectful but very honest talk with them. Tell them you’re worried about them and something needs to be done. Mom may be having memory issues due to the stress of taking care of Dad. It’s happening to me. Dad will probably protest that there’s nothing wrong with him, but you need to be firm. Offer to tour independent and Assisted Living places with them. Some are very nice. Reinforce with Dad that he needs to consider Mom’s welfare and safety.