If the son is on parole, you may want to try to contact his parole officer. I fully suspect that there may be conditions of his parole that may apply to keep him out of the park.
At the risk of sounding harsh, it is a fact that “sexual predators” are not a protected class under the state and federal constitution. In short, you can have rules forbidding them to be in the park due to the proximity of children.
If you don’t have such rules, you may want to enact some. But even though you don’t, I believe you did the right thing to require that he not occupy the home. You can and should do the same thing with regards to forbidding him to come into the park at all. If his family wants to see him, they can go to where he currently lives. The person(s) who has/have hired him to do odd jobs should be told that he cannot come into the park for ANY reason.
If you wonder whether this can be done without some specific rules, my response is that I would prefer rules to be in place. But even though you presumably have nothing on point, it would not stop me from banning him from the park. If he legally objects and wins, then it was a court that said he could come in – not you. Your main duty is to the park residents and their children. Better to try to remove him and fail than not to try at all.
Lastly, for your information, ORS 90.630(1)(c) permits a landlord to terminate a tenant if it is determined that they are “a predatory sex offender under ORS 181.585 to 181.587.” From your question, I could not tell whether the adult son was on the rental agreement, but if so, he is a “tenant.” The statute is not clear whether it can be applied to only a single tenant, without terminating the tenancy of the remaining occupants. Of course, the statute doesn’t address the larger issue of whether you may prohibit him from coming into the park, but I believe you are fully within your rights, as discussed above. However, you should first clear any such action with the park ownership, and they should secure legal advice on how to proceed.