Is the dog park close enough to the kids play area that my kid can play while I'm with my dog? 7 year old boy

No, it's by the back tree line next to the trails. If you have a friendly dog, most people dont mind if it's leashed on the playground.

You'd be about 200, 300 meters away, probably no. There is a path in the woods where could walk the dog and take your son, it doesn't go that far. There is a lot of grass between the kids' park and the dog park where you could play with the dog and watch your son.