Any new enough SUV with 6+ spd trans will tow better than you have now. Make sure you get something new enough that has 6-spd trans. That means 2007+ Expy, 2009+ GM twins. Or find a 2007+ Yukon XL Denali with the 6.2L/6-spd. It is a relative rocket.
I highly recommend the long wheelbase versions, Expy EL or Suburban/Yukon XL. The cost difference is negligible. The interior space is not, especially with the third row of seats in use. And the longer wheelbase is always a benefit when towing.
Spend $15 at a CAT scale to find out where you stand currently. 7k loaded TT is pushing the payload and rear axle limits with a family onboard of any half ton SUV. Half ton SUV payload seems to range from 1200-1600 pounds depending on brand and equipment. 700-1000 pounds of tongue weight eats that up quickly.
I love my 2500 Suburban. Essentially the same 2008-2013 models. While they are hard to find, so can be the half tons with proper towing equipment (axle ratio, towing packages/trans cooler, brake controller). Any every one of the 2008+ 3/4 tons come with what you need to tow a TT standard except the towing mirrors which are optional. Unfortunately, mine does not have the OEM ones. :( I had a 2003 F-150 5.4L before and get better fuel economy towing and unloaded, with far more power, gearing, and capability.