Ouch. FIL sounds like a pill, preemptively speaking for a number of other people and claiming there's no possible way they could have a good time while looking after their mother. This may be true, or it may be that one of the four would be perfectly happy to help out, and he's just assuming they won't. Very rude.
That being said, if Grandma needs full-time care at the party, I think you need to make sure someone is there to take care of her, before you consider inviting her. You can ask around the family as long as you don't pressure anyone; or you can hire the nurse/companion--who cares if FIL thinks it's stupid? It's not his party or his money. If none of her kids want to take on that role for the party, then they have no standing to say the hired nurse "won't go over well."
I will say, though, in my family, this is the point at which we generally stop inviting elderly relatives to parties--full-time nursing home care with confusion and serious needs. In my experience the person doesn't really have a good time--either they are out of it and don't remember/understand what's happening, or if they're still with-it, they're just worried about transportation and other issues the whole time.
Could you not invite Grandma to the party, but then later bring a little of the party to her, with DH, DIL, and a small number of other relatives going to see her at the nursing home?