Tow vehicles and large families are not easy matches. We only have 4 kids, and we've felt like we have few options ... 6 kids narrows the window that much further, so I feel ya. Honestly, the ratings of the 2500 Suburban aren't that great, either, and I suspect you'll be getting close to the maximum for a trailer to sleep 8, plus gear, plus bodies inside the 'Burb. I'll note that I believe you could reasonably tow that load w/ a 2500, but I suspect you'll be bumping on your max numbers.
What are your camping plans? How far away to you plan to go, and how often?
If you're mostly staying local (under a couple hours), I would by a used 1 ton pickup (should be had for $10-15k) for a dedicated TV. The 1 ton truck will tow pretty much whatever trailer you want, so you wont be limited to ultralights and so forth -- those command a pretty good premium, anyway. One of you drives the pickup and RV, the other drives your current 'Burb, and off you go!
Look at it this way -- a family that size can always use a spare vehicle or 2, anyway (I grew up as the oldest of 5 kids myself). Maybe the truck can be used by one of you as a daily driver or something ... they work as well to drive to work as they do to pull a trailer, after all.