Blimey, looks like the rules about transferring property are trickier than I thought! But if mum isn't paying rent to mb, he probably won't get as much out of the house as he thought her would if mum goes into nursing care.
Of course, if yb continues to take care of her, she might not go into care for very long and mb will benefit to the maximum later on. In a sense, yb is working for mb. He may want to think that over.
Does mb have poa over his mum's affairs? If not, then I don't think he can keep hold of the will. No one has the right to see it till your mil is dead, as a pp pointed out - sorry - except for the attorney and maybe, the poa. But unless that's mb, he has no right to have it either. Are you sure he does? Is it possible the lawyer has it?
But dh and yb may want to seek out more professional legal advice. It certainly can't hurt, imo. Nothing can be done while the lady is alive and the will, therefore, is not in effect. Well, nothing unless she were to change her will again. But, as you point out, she can't due to dementia. Legal advice would just be to give dh and yb the lay of the land and prepare them for what they may need to do when the sad day comes that the will matters.