Elder care and incompetence. Has anybody done this?

I had a coworker whose mom had dementia and refused care and became a danger to herself. My friend had to get a lawyer, go before a judge and have her mom declared incompetent so that she could get guardianship over her mother. She then placed her mom in memory care. It was awful. Her mom screamed and name called... it was very traumatic. If your wife is already in a facility, you may just need a declaration from a couple of doctors to take before a judge.

An elder care attorney can assist you with the legalities of everything.

It will need to be guardianship. If you don't do it, then the county will, and then that entity will control her portion of funds, and make all her medical decisions as well.

See the social worker at the SNF. Ask her if she is able to call a judge in your state for temporary emergency guardianship which you can later get in place permanently. If your wife is already incompetent there is now way she can assign you as POA. Do you have a will? They usually have a "springing POA" already there, saying what you need to take on duties as POA.
See an elder law attorney to arrange for conservatorship if funds are in your wife's name only and need to be managed for her care.

It sounds like you might need to file for guardianship. If she has dementia, she can't sign for DFPOA anyway.