Does my dad have to sell their house before my mom can go into a nursing home?

My dad is 81 and mom is 78.  Dad's health is ok.  Mom has nueroropothy and dementia and needs 24 hr care.  They currently live in an assisted living facility. Dad's mental state is starting to erode and he's becoming abusive with my mom. My sisters and I feel we should move my mom. Unfortunately we all work so she would most likely have to go to a nursing home. We're trying to find out legally what this means. Does my dad have to sell their house (which my nephew currently is renting) before my mom can go into a home? And what do we do if dad changes his mind once mom is moved? Help!!