When we were living in Maryland we camped at Lake Fairfax County Park, which is part of the Fairfax County Park System (Virginia). It was a nice campground with fishing, sports fields, picnic areas, and a water park in the summer. We were there during spring break of last year (early April) and the weather was pleasant. The park is located in Reston which is about 30 minutes from DC if there's no traffic. The park is situated in a nice residential area, and felt very safe. There was only one campground area open when we went, but there was a mixture of tents, RVs, and pop-ups. We tent camped in a site with electric hookups. HTH.
I too would avoid Prince George County, it;s not very safe. If you are looking at Southern Maryland you might consider Smallwood State Park, located in Charles County. There's a playground and fishing pier. It's probably about 45minutes south of DC with no traffic. Avoid trying to go to/from DC during commute hours. It would take DH between an hour and half to 2 hours to get home most night thanks to traffic.