Although neither hubby or I are only children, I can somewhat understand where you are coming from, and I sympathize.
Hubby and I just found out that his mother has hepatitis C. She is unemployed, lives by herself, and has no health insurance. Hubby has a sister, but she is pregnant, single, already a mom of a 2 year old, and just started a cleaning business with a friend (I have no idea if it is bringing in money or not) She has 3 sisters, one of who already cares for her dying husband, another one has a husband that suffered a pretty major stroke and needs assistance. This leaves sister number 3, who has major family troubles of her own and can't afford to take care of MIL. MIL is due to begin chemotherapy soon, and hubby and I are seriously considering the fact that someone may have to help take care of her (at least temporarily)...and that means us.
My mom also concerns us, but for different reasons. She is also single, but she works and has health insurance. She is 53, overweight, and just had a knee replaced...and may need to have the other one done. Strokes and heart attacks run in her family. Hubby and I know that if she ever needs to move in with someone, it will be us. Again, I'm not an only child, but the only child able to take this on. My sister has major health problems and can barely take care of herself and her family, let alone take on someone else.
This topic is definitely something I have thought about; I don't worry about it, but I think about it once in awhile and try to imagine what an addition to the household would do to our family dynamic. MIL and Mom are family; I have never considered having them put in a home (if it ever came down to that). As long as I can help them, I will.
As far as repairing your relationships...I have no advice, just encouragement. She is difficult, she is needy, she is driving you crazy...and she is the only mother you'll ever have (MIL's just aren't quite the same). Just love her the best you can