Will the nursing home take all of Mom's assets if I don't make the correct decision?

I have been Durable POA for my Mom for 8 years. I am also Medical POA and I took care of Mom for 8 years until she fell, went in the hospital, and is now in a LTC facility. It has been peaceful with Mom in the nursing home because my brother cannot harrass me daily since Mom is not at home. When I received the first bill from the nursing home of 10k plus I was surprised but not shocked. My question is this: my Mom has everything in her bank set up Payable On Death, transfer on death to my siblings and myself. She has the house set up TOD to me since I took care of her 8 years but I plan on dividing that if I should sell it later on. Is there a way to protect her assets with the high nursing home monthly bill? She has LTC insurance but it does not pay much (maybe 2k per month). Is it possibe to protect her assets (the savings, and her house) while I am POA? Also, she has been determined to be incompetent by her doctor and I have this paperwork. I would like to bring her home though she will require 24/7 care due to her delicate condition at 90 and dementia with pretty extreme sun downers. She also is the type that requires attention a lot or she will act out. I would love to bring her home but I do not know if I can hire enough people as she really needs a staff to be taken care of properly. She can walk with a walker but this is challenging as she has severe rheumatoid arthritis. She mainly rides around in her wheelchair. The skilled care stopped after day 22 and she was determined to be self pay. I appealed this twice but it was denied. I was hoping the skilled would last until day 100 but it did not. It is the hardest thing ever to have to make these decisions but if I make the correct ones then it seems like it will be okay. Thanks in advance for any advice from anyone of expertise on this matter or who has been there in this situation