I live in Staten Island. I can understand your desire to frequent dog parks.
However, I will warn you that dog parks are not the best places for dogs. It's a great place for the owners to chat, while the dogs ATTEMPT to establish pack order.... not happening.
My dog cannot enter a dog park. I've been observing her since a puppy, and the park dynamics are too unpredictable for me to ever feel safe for her.
I do make one on one playdates with a single dog that I know plays well with her.
To address your thread... You will NEVER get what you're expecting from a group of dog owners in a dog park. No matter what, you''ll get rude owners, aggressive dogs, dog fights, people bringing toys, and "in the blink of an eye" injuries.
IMO, you're better off either going for long walks with a dog-owner friend, or avoid that place.
Trust me, the way you describe it, it's an accident waiting to happen.