Short trip opinion

For the neices and nephews, especially at the tween age range, in many places you could rent two sites next to each other and bring a tent to put on the other site and split yourseves up among the two sites. You'd need one adult officially on each site. I doubt most parks would care in the least if both adults actually ended up sleeping on the same site so long as everybody behaved appropriately; extended family groups larger than six persons camp together frequently.

Having more than six people in a travel trailer is going to be mighty crowded anyway; you'd presumably need or want an overflow tent or something already.