Most modern SUVs are a lot more like cars than trucks - meant to carry volume, not weight. Most of them are unibody construction without a real frame.
The biggest problem is not power, but weight capacity. By the time you add tongue weight to the vehicle, there is nothing left for passengers or gear. Also, the short wheelbase can lead to stability problems. In general, the larger SUVs might be suitable for pop up trailers or very small travel trailers, but usually nothing much bigger.
If you have a big family and lots of stuff, look at the full size one ton vans ....