Should I have my mom's home put in to my name?

My mother has either early stage Alzheimers or Dementia-Dr's haven't totally pinned this down for me yet. She is taking Alzheimer meds but they don't seem to do much (if any) good, but that isn't the problem.
Two years ago my stepfather (her husband died) and left mom without any income except her Social Security which is about $1,000 a month, however he did leave her with TRICARE for medical (he was retired military) and medicare so she doesn't really have any major medical bills. She also was left with a mobile home on about 1/3 acre. Unfortunately it isn't paid off yet, she still owes about $10K on it.
All in all mom is in pretty good physical shape but her memory is pretty bad. She generally reminds me of a petulant child and it is very hard to make her happy. This is what makes me think it is early alzheimers.
My husband and I live within a mile of mom and due to her memory lapses I immediately started taking care of her bills and things like that. Within 6 months I realized I had to stop her from driving because it was a danger to others.
My husband and I live in a tiny mobile home in a senior community. We don't even have room for a nail to hang mom on so she can't come live with us. Also we don't own the land where our mobile is, we just rent to land.
I am one of 5 children that my mother had. So far she has outlived 3 of her children. There are only 2 of us left. My older sister lives about 100 miles away and basically only talks to my mom by phone maybe once a month. I am the one that calls mom daily, takes care of her medication, buys her groceries, takes her to the Dr, takes her cat to the vet, etc. But so far she has been capable of living alone. As time goes on I can see that it won't be long before that isn't possible. I also work a full time job and can't quit because I am the one that provides our medical insurance.
I have POA for my mom and she has a will which leaves her mobile home to me. She made that decision 2 years ago because she said I am the only one that helps her. She really doesn't have anything else of value to worry about. Recently I moved mom into a tiny little apartment so that we could try to sell her place. Mainly because she needed to be in a smaller place using less utilities and closer to neighbors for more companionship. I also figured if we sold it she could use the money to live better and hopefully continue to live independently with my help. I also figured that if she had to go to a nursing home eventually the Gov would take her place anyway. My husband and I have been cleaning and painting her place in hopes of selling it but it has been a few months with no real interest.
I can't afford to move into her place and lose my place if I will be thrown out when she passes or goes to a nursing home and I can't afford to pay for my place on the side. Things are very tight money wise for my husband and I.
If her place doesn't sell, the best thing would be for my husband and I to move into it and bring mom back to live with us until we can no longer handle her, but like I said I don't want to be left homeless.
I have been told that if the house hasn't been in my name for 5 years the gov can take it from me.
What should I do? Any help is appreciated. I can see this is rambling but I hope you can figure out what I mean.