Dad doesn't negotiate.
If baby doesn't want to come to the changing table, the changing table will have to come to him... Or something like that. I guess Daddy could carry the damn thing, but it's probably easier to just pick up the baby in question instead. Better for his back, no doubt.
"That wasn't a question, Bunny. You can keep playing with your friends when I've fixed you up. Get your pacifier and off we go. Or, if you'd like to keep fussing about, maybe we should just put you down for a little nap first so you can calm down a bit?"