Check with his local County Social Services and tell them he an elderly person who cannot take care of himself. They should provide an in-home evaluation and some recommendations for you. Stay on them and stay involved.
Many nursing facilities allow husbands and wives and long-time companions to share a room. Would this be a possibility? There also are facilities where the spouse/girlfriend can have her own room on an assisted living floor and visit him whenever she likes in the skilled nursing unit.
ask your father's doctor to request a home attendant for him so he can live with the home attendant and his girlfriend. talk to a social worker at the hospital . the idea of a nursing home sharing room your dad and his girlfriend is a good idea, too. social services also can help but I know that his doctor can prescribed home care and the social worker at the hospital will connect with a homecare agency or with a nursing home, what ever you want/decide