It's a tough situation. My MIL refused to put her mother in a nursing home. MIL insisted that her mother remain in the mother's home (out of state from MIL) long after the point where it was clear to the rest of the family that she wasn't capable of living on her own (cleanliness issues, not cooking for herself, letting bills pile up, etc.). MIL would say that it would kill her mother to go to a nursing home, that nursing homes were horrible places, etc.
It was clearly MIL's issue, as her mother would say that she would do whatever MIL (an only child) wanted. The family did convince MIL to hire cleaning help and someone to drive her mother around town for errands. When her mother died a few years ago, the rest of the family spent the visitation and funeral service discussing what a blessing it was that she had passed because her living conditions had been so bad.
Do you have other family members that could talk to your parents about the situation? IMHO, parents often don't listen to their children but might be more willing to hear it from the peers (siblings, cousins, aunts and uncles, close family friends). I wish someone else in my MIL's family had openly discussed the situation with MIL instead of whispering behind her back at the funeral how good it was that the mother had finally died.
I used to think that if MIL would just go look at the nursing homes (she had been in one 20 years earlier and refused to consider that facilities today could be better), she might reconsider. Could you take you parents, even just one of them, to visit the nursing homes in your area? Perhaps if they could see the alternatives, your mom would reconsider.
Good luck!