My sister and I found out my mom had stage 4 lung cancer by accident. They had no intention of telling us. I am not sure how long they thought they could do this. They (but mostly my dad) have refused most aid:
No to outside help, even for shopping,
No to medical alert,
No to wheelchair,
No to walker,
No to shower chair.
We finally got dad to agree to the shower chair after he got my mom in the tub and couldn't get her out and he is almost accepting of getting her a walker.
He is not in the best of health either and my mom's cancer has spread to her bones. I don't think she will make it to the end of the year and am really paranoid when hospice is suggested he says no.
I would say that worst come to worst, because uncontrolled bone pain IS the worst, your Mom should be transported to hospital by ambulance, and there you will need to work with Social Services and your Dad to iron out care options and plans. It may in fact be a Social Worker who ultimately calls you suggesting emergency temporary guardianship and in facility hospice. You cannot allow unaddressed suffering to go on.
Meanwhile you do not tell us that either of your parents are incompetent in their own decisions. If you take Mom to appointment or anywhere else, check with her that she is OK with what is happening. If not, it is straight to an attorney and POA being assigned to one of you with the second sister being an alternate. I am so sorry. There is honestly NOTHING worse than fear of unaddressed physical suffering in one you love. I hope you will update us and wish you the very best.