Hi Judy-
This is an odd and very sad situation to say in the least. When my grandmother had to go into some kind of assisted living, my father and his two brothers got together and chose a place that was within all of their budgets. Each brother paid 1/3 of her costs, and the living that my grandfather had set up for her before he died paid all the extra expenses. I truly believe that that is how it should be.
Before my grandmother moved into a facility, though, she lived with my family from when I was 4 until I graduated highschool and was into the junior college. My parents decided that since my dad's two other brothers did not want her staying with them, that since she was capable, needed to find an apartment. They found one in her price range that would still allow her to keep her car, buy groceries, etc. However, we had to go with her alot of times to make sure she didn't overspend, etc. It was very hard on my parents that my grandmothers 2 other sons thought sending a check once a year was enough after caring for her for so long. She had so many health issues, both physically and mentally.
In your situation, I would see if you could bring her into your home. It's alot of work, but it may be worth it. She can contribute maybe $100-$200 to groceries and utilities and be with her family all day. If your brothers made the decision to help her under the assumption that you had the spare cash, that is a huge faux pas on their part. However, to demand you pay them and limit your contact is petty, and they should not be allowed to treat you, your sister, or your mother that way. As far as kicking their own mum out..well, I have a number of thoughts on that one....
If you or your sister can, I say take in your mother. It's a tight squeeze, but at the end of life, elders should be with the family that loves them. It will strain you, of course, but not enough to where it's not worth it. I know you don't have any extra room....we didn't either. But the few extra hundred that my grandmother contributed allowed for a little more stretching in the living situation. Plus, your kids can learn some valuable stuff and spend some quality time with your mom around. I hope that helps. Ask your mom if she would be willing to use a portion of her earnings to help you rent a larger space where she can have her own room, especially if she is going to be around for a while. If so, then make preparations to move. OR, ask your sister if she has a spare room or would be willing to do the same.
All in all, don't spite your brothers, but do let them know what you are doing when the decision has been made and if they would like to contribute, they can, but it is not necessary. Be the bigger person. =) I also saw a great suggestion below about assistance for elders who are on limited incomes. I know that in my town, they built new low income housing that is severely nicer than my home. I wish I could move in!!! I also know that the state offers a once in a lifetime use, emergency housing assistance. They place you in a home immediately (usually an apartment), something in your price range, and then like low income housing, charge you a percentage for your rent based on your income. Your mother should qualify.
I really hope that helps. Good luck, and take a deep breath. It will all work itself out. Your brothers can't force you to pay as you never agreed to it. Don't sign anything with them, and don't verbally let them force you into agreeing to pay. While their income may be limited, yours is as well. Next time they should talk to EVERYONE concerned before making a decision about your mom and let them know you are happy to discuss options. Life is like that, and you want to help but are limited with your own resources as well.
-E. M