$10 says its your tires. If they are P tires (passenger car) they will ride sloppy especially when you try to tow or haul something. Most SUVs and some light pickups come with P tires cause they are cheaper and ride softer for all the vag that drives trucks these days.
Besides proper LT (light truck) tires, if your tahoe needs anything more than new shocks then theres probably something wrong with it. It shouldnt ride that sloppy.