They can TRY to ban someone from public property, but it's not going to be easy to do. Ultimately they will have to go before a judge for the order to be enforced. However, even if this is not a legally enforceable order, the involved juveniles should stay away from the listed places unless their parents are prepared to pay for attorneys to fight possible criminal trespass charges or to fight a restraining order in court. They made a decision to create an "incident" that sufficiently pissed off the city fathers to get the mayor to ban them from public property. That should be a wake up call.
Perhaps the parents of the children can go in and talk to the mayor and ask about what can be done to allow them access to the parks again. Also, why does it concern you that these kids do not have access to the police department or the traffic court?? I doubt you have anything to worry about there ... if the police arrest the kid and bring him there, that's on them. And if he has to go to traffic court then that should also be an exception. Hopefully he's not that big of a troublemaker. But, maybe he is.

