I would tow that TT with my 2011 3/4 ton Suburban. If you are having troubles towing with yours, it is likely a weight distribution issue, either not enough TW or poorly setup WDH. But I have a suspicion that the wife's company Suburban is the half ton rated only to about 8000 pounds and closer to 1400 pounds of payload. If that is the situation, then you are likely over a couple of it's ratings when loaded for a long weekend. Count the lug nuts or check the tire and loading sticker to confirm the half on vs. 3/4 ton Burb.
You really want a TV with at least 9000 pound tow rating and 1800+ pounds of payload. There are some half tons that fit that, but not many. Meanwhile, every late model 3/4 ton crew cab pickup would work well.