Your father needs assistance in his living, but doesn't want to go to an assisted living facility and hopes this arrangement with the widow will somehow permit him to live independently? But he knows your mother would object, find it unacceptable, and refuse to go along with it? It seems to me that he needs to think about a living arrangement that is acceptable to your mother, even if that also means it is somewhat less acceptable to him. They've been married for a long time, so I assume this won't be the first time he's had to compromise.