Where can I find the water where I see everyone letting their dogs swim around?

Try around the paddling access points like the the valley paddling access point

There is a creek down the hill from the concrete path that circles the splash park. If you are in the parking lot of the Splash Park it would be to the left . The creek runs all through Broad run.

Dogs are supposed to stay leashed in the parks

Yes. Brilliant observation! Google earth app?