Can the nursing home kick my mom out if I am making payments towards her past due amount?

Medicaid, Medicare doesn't pay for long term care. Housing and food portion anyway.

Did you sign anything to agree to pay out of your own funds for Mom’s financial obligations? If not, then you aren’t responsible. However, since you already started paying, you’ll most likely have to continue. How will you meet her future financial obligations? Speak with the facility’s financial officer and ask if as long as you paying down her debt, they will keep her. Also, ask about applying for Medicare for her future bills.

Yes, that’s what I meant. Thank you.

Medicaid is paying now I just have to pay the $2,800

Have you had a sit down meeting with the accounting manager and demonstrated your earnest intention to pay? $2800 is not a huge amount when looking at the big picture, I think you should be able to work something out.