It doesn't matter whether he was invited or not - if he is the bio dad and has some sort of custodial rights (which it appears he does), then he is legally obligated to sign off on a wish, and in fact he is the person who "should" be going as the second adult participant per MaW guidelines.
As for his comments about only being for kids with six months to live, that tells me he wasn't invited in on any of the discussion with the MaW people at all. They're incredibly quick to correct that misunderstanding. If he didn't sit in on that, then I can understand a whole slew of problems coming from it, including issues with wish participants and travel waivers.
If I were going to guess, I'd say the issue is probably about does dad get to go as one of the two paid adults instead of the grandmother, and that's something a.) the mother and father should have worked out together and b.) absolutely has to be settled before the trip planning can happen.
This is actually more common than most people realize, especially in situations where you have divorces and step-parents, but most parents keep it out of the media and eventually settle it behind the scenes. I don't know enough about the family dynamics to know who is "at fault," from the mother refusing to let the father visit or the father legitimately being uninterested, but I do hope it will get worked out.
I do find the donations bit a little bit odd though. Odds are they will eventually get this worked out and she will get to go on her Wish trip to Disney. Why collect the money? It's not like because it's delayed right now it will never happen. Also, it doesn't make sense that they yanked the wish request. I know lots of wishes that sat in limbo for a year or more because of paperwork issues and participant issues, and this could have almost certainly happened in this case. There's a piece missing there that doesn't involve the father refusing to sign paperwork to let his child participate/the grandmother go in his place.