A dog park is supposed to have barking dogs.
It’s where they go to play and be vocal.
They aren’t allowed to be overly vocal in their own back yards as the neighbors would complain; so ticketing a dog for barking in a dog park is touching on lunacy.
Perhaps the overly sensitive neighbor who complained, needs to move away to a different neighborhood and live where there aren’t any parks or people too close to them.
It would be best for all concerned.