THe problem is, if you don't have a fence, it's pretty hard to expect people to stay away, or even really keep them out.
I think that with some families, they kind of feel their kids have a right to run around and they aren't very concerned about property lines - 'we came out here to enjoy the COUNTRY', basically. And of course in the country, no one cares if you go play in their stream, right? You might hit a little of that attitude.
Well, I think the best thing you can do is put up a fence, and put up on trespassing signs on it, and send a very friendly kind letter to each neighbor in that 'freedom kid' area.
''Hello Neighbors, I am your new neighbor Mary Smith at 100 Children's Creek Lane. Since I have my pets and small livestock on the property, I regret I will have to put up a pasture fence on the property line that will unfortunately make the creek inaccessible to your children. I'm sure you understand that I can't have the children on the property with my dogs and livestock. Thanks! Mary Smith'
With a fence up, you have more legal recourse. If you don't have a fence, the creek functions somewhat as an 'attractive nuisance'.
I don't think it really needs to be a huge fence, but some posts and chain or welded wire fence might not be too expensive. Another cheap alternative is wood posts with fence boards (planks) ontop and electric wire every 10 inches or so. Electric fence tends to do a good job at keeping people out.
The OTHER option you might consider, is letting the kids have access to the stream, and not worrying about it.
My guess would be that for a while, it will be cute. Babbling voices on a Sunday afternoon, sort of cute. But eventually they'll get up or teens will start stopping by at 2 am, the beer cans and the trysting in the bushes will start, and you will wish you never did it.