^^ Took the words out of my mouth, regarding wheelbase of the Tahoe... i.e. the distance between the front and rear wheels. It's fairly short, compared to its longer cousin the Suburban (or Yukon XL on the GMC side) which will negatively impact the stability of handling the trailer... especially longer models. That is just one of several factors, but one that is often ignored.
I completely understand the need for 3 rows of seats and extra people-moving capacity. We are a family of 5, and until a few months ago I towed our 32' TT (weighing a little over 9000# fully loaded) with a 1995 Suburban 2500. That's a 3/4 ton version, which is pretty rare but they're out there. I'd recommend looking to buy one of those, if you want to be sure you have a stout SUV to tow your trailer. Up until 1999, the strongest powertrain combo was the 7.4L engine and 4.10 gears, which is what I had. All 2500's (whether pickup or SUV) had the 4L80 transmission. That had a 10,000# rated tow capacity, which was bumped to 12,000# in the 2001-2006 models when the 7.4L became the 8.1L option. In 2007+ models, the largest GM truck engine became the 6.0L and lost the higher-end towing capacity... maxxing at 9700# with the right options. I believe that eventually the Suburban 2500's were no longer offered except perhaps by special order and fleet use, but I hear they've come back again as of 2018 or so. Still rare I'm sure, but you may find one if you specifically search for one.
Now that my kids are older and more tolerant to longer trips, I decided to go "truck" so I can stop worrying about TT tow capacity and prepare us for fifth wheel ownership in the next couple years. My new-to-me 2005 Silverado crew cab diesel dually fits that bill nicely.
Yeah it'll be tighter fit for 5 of us in the truck, but it's still quite roomy and technically seats 6 with two benches. We are weekend/vacationers, so overall it will only be a few times per year that we'll all be riding together for lengthy periods.