My elderly parents live in their own house. One has dementia and diabetes, is very stubborn about the possibility of going to assisted living. The other is in her 90's and is showing signs of cognitive degeneration, and wants to go to assisted living.
We pay for their co-pays at the Doctor office or the emergency room since it is easier with a debit card. They are on a fixed income and most of the time, they think that they have already paid us back. I don't disagree due to the dementia.
BarbBrooklyn is correct in asking if you are the PoA for either of them. Your Mom may still be able to legally assign you. If your Father has just the beginnings of dementia, he may also still be competent enough. If not, the only other option is court-ordered guardianship, either by you or the county.
Consider calling social services for their county and talking about options with a social worker.
You should be able to pay using their credit/debit card or reimburse yourself.
Are they on Medicaid?