My Mom has dementia and I can't handle the snarky, bitter woman she is.

My Mom and I have had five fun years living together. We have enjoyed each other's company, and really become friends.
Mom and I were not close at all when I was a child. My father was the loving parent, and Mom was always angry about something. After my father passed away and I got divorced, our relationship grew. Mom is 77, and I am 53.
Mom's health has always been really good. Mine is not so great. I have a lot of anxiety. My knees need to be replaced, and I am in constant pain. I just never got around to fixing them while she was able to help me. Now I can barely walk.
Last year we had a change in our family that sent us both into depression. We both have always had depression, runs in the family. Her health has been on a downward spiral since last June. She has had 2 hospitalizations. The first due to dehydration and the second due to a TIA. Following the TIA, she was in a rehab to help strengthen her body. Mom has never been very active, so she was weak to begin with.
During her stay in the rehab she went BONKERS! She was so angry and mean! My daughter had a baby out of state and I went back to be with her for 3 weeks and Mom went postal. Her dementia and her already bitter attitude are not a good combination.
During her time in the rehab center, I had a little emotional breakdown due to everything that has taken place over the last year. I have been off work for 6 weeks, and I am scheduled to go back in about 10 days.
I brought Mom home from the rehab yesterday. She had made an amazing change the last week in the rehab, and she was happier, and doing physicially amazing. So, I thought that bringing her home would be great. She would be happy and I could handle it. What was I thinking?? She is physically so much better than she has been in years. She can out walk me by a long shot. But, she wants to be waited on hand and foot. She is bitter, grumpy, (snarky) and very selfish. She doesn't care what anyone else wants or needs, it's all about her. She isn't at all happy about the new baby, and couldn't care less about anyone but herself. I know in my head that it is the dementia and her normal way of thinking. Or, back to the way she was when I was younger in the grumpy way.
If I put her in a care center, she will be angry and very unhappy. She dosen't have the funds to pay for assisted living or a really nice place, but her income will support her in an average care center. But, is that the right thing to do? I don't really want to live like this for the next 10+ years. I want to have somewhat of a life of my own. I feel trapped. Am I terrible for wanting my own life now? I raised my kids as a single Mom, and now I feel like it's my responsibility to care for her. But I am not doing it because I want to, I feel like I have to. Is it selfish of me to feel this way? Having her go into a care center will certainly change my lifestyle monetarily. We share the rent and the living expenses.
What should I do? HELP!!!