Assateaque is a fantastic place. But it is difficult to get a site . Especially during peak season. There are only a few sites with electric.If the OP is lucky enough to get a site with electric Assateaque is a decent choice.
However Frontiertowne is about 15 minutes away it is very family friendly with an on site water park.
More importantly water/electric sites are available. Summers in MD are no fun without A/C. If the OP can do without A/C Assateaque maybe choice #1. But if the OP likes A/C like I do Assateaque will be great for a day trip or a beach trip. But Frontier Town will make a much better base camp.
Delaware Seashore Park is a nice alternative. Full hook up sites, walking distance to the beach from your campsite