What are the legal responsibilities of adult children when one parent refuses to get adequate help for the other parent?

My mother is 85 and my father is 91 with dementia, they both still live in their home. My mother has a caregiver that comes in M-F for 4 hrs a day to help with my father. Since my older brother passed away in December my father has been falling more and having incontinence issues day and night. My mother is physically and mentally declining and is suffering from major depression, this is the 2nd son they have lost. My sister and I are the only children left, we make sure they have plenty of prepared food but my mother may or may not fix it.
My mom does not want to go to assisted living (it is fine for all her friends but not her), she does not want to put our father in a memory care facility and she cannot afford the $16,000/month for 24 hr care in the home.
My sister and I completely understand what she desires but we are also very worried that she is not capable of taking care of our father and keeping him safe. We do not want to get into a legal battle with her but we also don't want to be blamed for not stepping in and "doing something" about their situation when something bad happens. We want to keep both of them safe and give her some relief of taking care of my dad.