It would be good to know what your payload capacity is. Drive your Suburban with your entire family inside and get it weighed at at scale. I agree with the others that you will probably go over your GVWR or rear axle rating before you hit your tow rating. Guessing, 5-6000 lb loaded trailer will be about your max due to your large family. I have 3 kids and we just bought a 2500 Suburban because I figured we're already at a max on a 1500 Suburban and would easily go over its limits and eventually would. Smaller hybrid might work well or a simple bunk trailer with no slides.