If the Suburban doesn't have the heavy duty tow package, it won't get the job done. We have had 2 Tahoes with the tow package and they are rated to tow about 8200lbs. Without tow package it's rated for like 5500lbs and will definitely not do the job. Suburbans have similar ratings, but actually a little less than the Tahoe because the Suburban naturally weighs more. The biggest issue would definitely be payload even with the Suburban with a tow package, but if you had less than 1000lbs of tongue weight and nothing in the vehicle, but 2 adults and 4 super light kids you'd probably be right on the borderline on payload/axle weight. Just make sure to keep all your accessories and what not in the trailer. If you'll be towing into mountainous areas, it'll probably struggle, but on flat land you could probably get away with it. My Tahoe is on the border with all the weight ratings, but I've towed all over the country. I've been looking to upgrade to a Suburban 2500, but finding an LT model in my area has proven difficult. Once I locate one, I'll be upgrading. I need the room for dogs and people.
If you're purchasing the Suburban, I'd try to find the Suburban 2500. If you're borrowing it from a friend or something, make sure it has the tow package. Otherwise, you're probably looking at 2 vehicles OR trying to find a 2500 level or higher van to rent/borrow.
2010 Chevy Tahoe & 2015 Keystone Bullet Premier 30'