Both parents live with me in Virginia. My father is on in-home hospice. My mother has power of attorney for my father, which she obtained in New York State when she sold the house. I have power of attorney for my mother. But I fear that if my mother becomes unable to be the power of attorney for my father who can act on my father's behalf? I will be meeting with the lawyer who drew up the POA for my mother to ask what I need to do to be legally responsible for him.
Your father is on hospice. Is your mom not competent to make decisions as needed?
Does she have Financial and Medical DPOA?
Look for the online videos that explain guardianship. You may be able to find the questions you want answered, clarified, or need to ask there. Laws may vary from one state to another.
Find out if you would need to file for each of the LO in two separate cases or if it can be combined somehow. Check into financial separation. Check into signing legal documents, including the IRS. I filed an IRS form available online for signing tax returns. SS is another thing, discuss what you may need to do for SS. Ask how to handle bank accounts with the lawyer and the banks.
Hope this helps you some and best of luck.