The best SUV for those trailers is a 2500 series Suburban. They stopped making them in 2013. However, in 2007 thru 2013 the hitch was limited to 1,000 pounds of tongue weight which really isn't enough to be able to take advantage of their 9,xxx pound tow rating.
If you go with a 2001 thru 2006 2500 Suburban with the 8.1L big block they were rated to tow up to 12,xxx pounds and didn't have the same limitation on tongue weight. So, that would be just about your only choice.
The other option is a Ford Excursion made from 2000 to 2005. If you go this route look for one with the V10 gas engine. The 6.0 diesel is a nightmare. A very few had the 7.3 diesel which was a good engine but quite old in design, and loud. Despite that, since they were far more reliable then the 6.0 diesel they command high prices.
If you don't like any of these choices you can go the van route. Which isn't bad, I'd get a Chevy with the 6.0 gas or even a Duramax.