Well I live in Western PA and I know of a few good ones.

The one I recommend is Cooper's Lake campground. They have everything you requested. A park for kids, a lake for fishing and canoeing (not swimming due to Snapping turtles), and they have RV sites. It's right off 422 so you are a short drive from Moraine State Park which has beaches and is a great place for kids. (Cooper's lake is closed from now until I believe the first week in august for a big convention they hold there.)

A campground I went to as a kid and LOVED LOVED LOVED it was the Erie KOA. It's a great place for kids and parents. They do have RV sites, they allow pets, and they have a pool, a pond for fishing, an arcade, and a small petting zoo (just like 2 goats but it's fun). I REALLY RECOMMEND THIS ONE.

It's a short drive from Lake Erie which is a great place to go swimming especially for this season because the water is warm. They also have a pancake breakfast on sundays and they hold a movie on saturday nights i think. I haven't been there in a few years but I have the best memories from there. The employees are the nicest people and they keep the campground really nice. The bathrooms are nice too. They also have a laundary room and a nice store. It's about 20 minutes from the peninsula and erie so it has a great location.