Welcome from White Plains, New York.
Here is my advice. Put your freaking video camera away, say "Yes Sir," and leave.
You need to use your head as well as your machine. If you are going to detect in a heavily used and patrolled public park, you need to be there at first light, and leave by 7:30 am. If you feel the need to rely on US to tell YOU what the laws are where you live, in my opinion you are in the wrong hobby.
Now, I know a lot of you are going to say I am being too harsh - or maybe even a complete ***hole. I can understand that. What I don't understand, is how so MANY newbies and veteran hobbyists alike, think it is OK, or even their "right" to detect a busy park, totlot or beach, at the busiest times of day. I have been in a park with my kids at 10am, and watched a guy swinging in between the picnic blankets and digging holes two-feet from folks trying to enjoy themselves. Same thing at the beach with morons detecting in the dry sand literally right next to people, their blankets and chairs! Is it any wonder most of the population thinks our hobby is rapacious and predatory?
If you can’t figure out what is wrong or right, legal or illegal all by yourself, then find another hobby. Yes, I know I sound frustrated, because I am. Common sense people, common sense! OK, I’m putting on my flame ******ing underwear and readying myself for the discourse that is sure to follow.