My Mom's (92) showing signs of dementia, which has been going on for the last couple of years. Advice?

She lives in her own home with 3 cats and has many outside cats too (fleas also). She has lots of stress with going to the doctor and thinks that we are going to take the cats away from her. We are trying to make the house safe and clean but she fights us. There are 3 female siblings but the youngest because she lives closest get the brunt of it. We all have jobs so we hired the neighbor to help take care of her which is working out well. The problem is that mom stresses over the cats and won't cooperate is not feeding them wet food that makes them throw up and trys to go out the door to feed the outside cats even though we tell her we feed them (which we do). Just Monday she fell out the front door and thank God did not get hurt. As I am the oldest I am trying to convince my sisters that she needs to be evaluated so we know what stage here dementia is but they don't think it is necessary as we know it is dementia. I am the one who lives 1 hour away so it is hard from me to help more. Anyway, my younger sister thinks that if we push the issue on the cats (not doing what mom wants) we will be participating in leading to her death. The problem is that mom is leaving in the outside cats, the cats are peeing, there are fleas and it is a mess and I don't know how best to help everyone. Any suggestions will help. Thanks.