A couple more questions to help get good answers:
What type of towing, several times a year for only a short distance?
More travel over longer distances? Flat land or mountains?
There's a lot more involved than just towing in a straight line.
Well the Tahoe be able to control the TT in an emergency situation? Remember a Toyota can pull the Space Shuttle.
I personally wouldn't, but I tend to go overboard anyway. We had a 91 Fleetwood Prowler 24' TT, no slides just a very basic TT. We were towing with a Silverado
1500 Heavy Half 5.7L with full towing package. It handled the TT but it wasn't a fun tow, at the same time we also had a 2004 Trail Blazer that per the GM numbers said it could handle the Prowler, but knowing how the 1500 handled it I couldn't even image putting it behind the Blazer.
So at the end of the day, only you can make the decision of what's right for you and your family.