From what you are saying, I would suggest that you looking into Sterling State Park Sterling State Park Detail
While the RV park is little more than a parking lot that has some FHU sites, many have fire rings and picnic tables. The rest of the sites have electric only (30A). There is water and dump at the park entrance road. There is also a swimming beach on Lake Erie and kids play areas (closer to the day-park area). You will have to bring or buy firewood for smores. I suggest you look over the pit before you build a fire, I have found some where plastics were burned. Few sites are actually water front.
Small problem, it is 50 miles (south) from the Zoo.
Camp Dearborn is closer at 30 miles and is a very nice place, but it is 30 miles the wrong way. There is a nice beach and play area not far from the FHU sites.
1 - If Missy is a pet, no pets allowed.....
2 - I do not recall fire rings. They may have, but I don't remember.
Detroit Greenfield is 40 miles out I-94. It used to be a KOA, but no longer. OK for kids, but not much water.
There is also an RV resort place real close to Monroe, but those are places we avoid.