My advice to the LW would be to leave the planned money distribution entirely out of the discussion about how LW's mother will be looked after.

THIS. I don't think the advice in the letter is a good idea--it makes it sound like going into assisted living is punitive, retribution for an undesired distribution of her assets, and, okay, maybe it is that in LW's head, but treating it that way is going to make it even harder to convince the mother to embrace assisted living.