^^^MayDay gets it. After re-reading this thread, I am convinced that the posters recommending compact wagons and crossovers either have never transported two kids plus camping gear (nevermind two dogs) or enjoy a different version of camping than me. Which is fine, but the OP should realistically consider the volume and the shape of the stuff they want to pack.
We had a euro status wagon for a couple of years with two kids, and it was workable but not fun for camping trips. Even with a generously sized roof box and the ability to put bikes on the roof at the same time. Packing both the roof box and trunk became a Tetris-esque exercise that was all well and good until we wanted to stop on the road and pull out the food, dishes, and camp chairs for a picnic lunch or gear up for a bike ride or hike. I'm also convinced that we blew the water pump (among other things) from repeatedly powering up and down I-70 and other Colorado highways in this fully-loaded state, but that's another story....
Items that made a wagon challenging for us included various combinations of our cooler, 7-gallon water container, kid carrier backpack, bikes and associated gear (x4), camp chairs, firewood, and fresh, delicious food and beer for 2-5 days. I consider most of these items necessary for the places we like to camp. You might not need any of this, though.