My Mom needs more care than my sister and I can provide. What help can we get with low-no income?

8 months ago my sister, her boyfriend and dog, plus my mother and her dog all moved into the 3 bedroom house I am renting with my friend and her young daughter. This was supposed to be a temporary situation that has transitioned into a permanent one. My sister, room mate and I all work full time, the boyfriend doesn't and thinks that emptying the garbage and picking up dog poop is enough to cover the resources that he uses. My mother can no longer live by herself and has gotten increasingly worse over the last 8 months. She spent 2 weeks in the hospital after emergency surgery for a ruptured appendix that she refused to be taken into the ER for over a week. I knew something was wrong but she refused to go. I tried everyday, she was practically unconscious when I took her in and according to her surgeon she would have died if I had waited any longer. My mother has been diabetic since she was a teen and has had a kidney transplant after years of dialysis. She refuses to eat properly and since her ruptured appendix has been incontinent. She needs a walker and still has fallen several times. My mother and sister think that moving into a different house will be the solution. Realistically this is not a solution as we could not afford a place that will allow 2 big dogs and 4 adults. My mother has applied for SSI we have yet to hear anything back and is currently on several low-income programs. She has no savings or income and is not able to work. My mother has never been the easiest person to get along with and has a history of depression and alcoholism. Our family has a history of Alzheimer and I am concerned that she has been exhibiting signs. Our current situation is no longer sustainable and needs to change. I don't know how to bring this up with my family and need help. I don't want my sister to be solely responsible for my mother, I don't feel that is the safest choice. I am afraid that she will be angry with me and try to take it all on herself. I am 27, my sister is 23 and my mother is 56. I need help.