Newbie and can't figure out the "What can I tow" math

The cargo rating of your Tahoe will be the limiting number. Considering that loaded trailer tongue weight will be around 1,000 lbs + your 600 family = 1,600 lbs before you load other cargo. The drivers side door sticker on the Tahoe will give you the load or cargo carrying capacity. I suspect you are marginal at best. Too much trailer or too many folks depending on how you'd like to spin the situation. Can you sneak off without the kids? Just kidding, but you'll likely have to reconsider.