First thing you and your Mum need to do is get her to see a lawyer in order to understand what needs to be done. Then put things in place. Each state maybe different and the laws continue to change. Have a will in place. Have you done yours? Name one or two people who can have powers of attorney for her should she become so unwell that she can no longer look after her own financial affairs. The name executors.....etc. The list is can be quite extensive so for this reason you need a lawyer.

It is important for her wishes to made made known now that she is still alive and sane. It's nothing that nobody likes to think about but is so helpful when the time does come that you know what needs to happen and the wheels have already been set in motion not while you are in the throws of grief.... etc.

We always expected that my father would live the longest. Mum was always unwell. Dad though had cancer and passed away in 6 months. He didn't go into a nursing home but our Mother was in one for 4 years before passing away.

Are you sure you mum is going to go into a nursing home? Where I live nursing homes can be state funded or privately funded with the nursing home retaining a bond (very large) but at the end of it they will/should refund the balance. Please get your lawyer to take due diligence and look at the nursing home paperwork. Often the devil is buried in the detail.