If I am to recieve the home after death, can I take out a mortgage to continue to pay for care in home for Mom?

Consult with a expert on this. If the mortgage is in mom's name only and she dies, they may call the entire thing in. There are some protections for spouses on mortgages when one spouse dies, to allow them to keep making payments, but I'm not sure about adult children. I'd make sure. There are other considerations as well.

Like what if something happens and you become disabled and can't make the mortgage payments? The house would be foreclosed and nowhere for you mom to live.

Also, paying the mortgage would not likely give you any property rights to the house, though you might claim an equitable interests. Still, it's too risky. I'd see an expert on how to work this out the safest way. The house may be exempt for Medicaid purposes now, but if there is cash in a bank account in her name, it could cause questions. Because things are so picky when it comes to finanical assistance, I would fully explore the implications before I did anything.

Whomever owns the house is the only one that can take out a Reverse Mortgage, or an equity loan, or re-finance said property.

First, is your mother receiving Medicaid, or is she likely to need to apply? Have you been providing caregiving assistance for your mother such that you have prevented her from going to a nursing home for 2 years or more? (If Medicaid is not in the picture we don't have to go into those details.)

Do you mean that Mom would take out a mortgage on her house and use the money to finance her care, and then when she dies you will get the house and either pay off the mortgage or assume the payments? Or perhaps you would start making the payments now? I'm not sure that you can take out a mortgage on a home you don't own, but perhaps you can cosign the loan if Mother can't qualify for it on her own.

As POA your sister has no influence over what is left to whom in a will. But she does have responsibilities regarding Mother's financial transactions now. How does she think Mother's care should be paid for at this point? What are her suggestions for financial management and disposition of the house?