We pulled a 17' Casita with our TDI converted Tiguan. CJAA with 6 speed, towing springs and Bilstein shocks. We went all over the Southeast. It did fine except it did not like starting on on incline, say taking off from a dead standstill in the mountains. We eventually went to a TDI Touareg which did much better, it's rated to tow 7700 pounds. You have to be careful on either with tongue weights. Europeans get by with way less tongue weight than yanks do. So yes I think your wagon would work, although the mountains near you are probably much worse than we would encounter in the Smokies.
So now, lets talk campers. The Casita and Scamp are fiberglass campers, very well suited for smaller vehicles. It was just my wife and me in the Casita and it was tight. I think you would have a tough time in the 13' Scamp (or any other 13' for that matter) with 3 kids. Casita (and probably others, but I'm more familiar with the Casita) make a model with bunk beds in the front, but you give up the bathroom. With a small camper, you have to decide what you want. Honestly with 3 kids, I would lean towards a bigger unit, which would pretty much eliminate towing with the wagon. Really a 16' unit would be better towing wise, but it's even tighter. We ended up getting a motorhome, which is much roomier than the compact campers. The Tiguan has become the toad (camper speak for the towed vehicle) so it's sort of come full circle. It's a lot higher cost, but if you plan to use it frequently and keep it for a few years, that might be the way to go.
I suggest you go look at some units and decide what will work best for your situation. There are no perfect solutions, all of them have advantages and drawbacks. It's what works best for you.
