Assisted Living, Memory Care, or Nursing Home?

My 78 year old mother has advanced Alzheimers. She currently has 24/7 care and cannot do anything independently. She is incontinent and also has vision and mobility issues. She cannot walk on her own, is unable to use a walker, and will probably be in a wheelchair soon.

I'm guessing assisted living places would not take her based on her condition. She doesn't have complicated medical issues that would require a nursing facility, but I'm unsure if memory care facilities would take her due to her mobility issues. For example, if she is lying down on the couch, she cannot sit up on her own. She can occasionally go from sitting on the couch to standing up on her own but is generally uncooperative when we want her to move around.