The hunter and the dog are separate "characters". That is what I got in mind, correct. I control the dog but not the hunter. The hunter finishes the dog's work by shooting wherever the dog is pointing at. Correct, just how I had in mind.
The specials (except recovery move) you described pretty much match how I envisioned them. The recovery move I had in mind was the dog flying away with ducks... just like in that Crusade video. It's just too good.
I was thinking that the ducks could be somewhat like disjointed hitboxes? Like, when the dog uses a duck as a bludgeoning weapon... and if a character shoots a projectile at the dog... and if the dog uses a punch or a kick on the projectile, the dog gets hurt... but if the dog uses a duck, only the duck gets hurt.
I was also thinking about Snake's Smash Up move where Snake shoots a missile upward and it goes back down... this missile has its own disjointed hitbox. Now, picture this missile as a duck. If the dog's Smash Up move is releasing a duck... the duck flies upward, maybe in a zigzag pattern like you described, and the duck pecks anyone who is in the way till it flies offscreen (flying away just like in the NES game).
I also liked this move the dog did in Crusade... it looks like it might be Aerial Forward+A (Meteor Smash?)... anyway, what the dog does is he pulls out a duck, swings it like a bludgeoning weapon, and then releases it. The duck flies away upward... now it is a flying disjointed hitbox.
Welp! I think Duck Hunt Dog might be a tricky character to use with all these
flying disjointed hitboxes ducks.