Can I Legally Take Control From My Mother?

Location: Illinois, USA. My mother is the executor of her parents' estate. They are both passed now, but my mom neglected to file their will with the court. She is being sued by the bank for the remainder of the mortgage ($10k). The nursing home will likely follow, there is a balance of $45k. My grandparents only had the house, there are no other assets. The house is not worth very much at all. All life insurance had already been given to the nursing home. My mom says that there is an annuity worth around $20k but she can't get the company to release it. They just keep asking for more paperwork. She wants to use it to pay off the bank, and then sell the house to pay off the nursing home. The estate still needs to go through probate. What do we need to do? My mom cannot handle this by herself. She seems to be in a depressive/paralyzed state. She still speaks in the present tense about my grandparents, can't stay in a conversation without going off on irrelevant tangents, and seems incapable of settling the estate by herself. My sister and I want to work together to get this settled, but so much requires my mother's cooperation and that is drawing everything out and making it worse. The lawyer we reached out to wants $2k up front and none of us have that. I just lost my job, my mom is on disability SSI, and my sister is a low income disabled veteran. We have a court date on Jan 20 with the bank and the mediator. I want to take over as the authority for their estate and get this settled, my sister supports this. What can we do? Do I need to get her mental capacity checked? Can she sign rights over to me? I think with a heartfelt conversation I could get her to do it, we are all on good terms and in agreement. I'm afraid this whole situation is going to ruin my mother, and I just want to take the burden.