Few tips I have,
Keep the motor in the power band when towing... I like to keep mine in the 2-3k rpm range when towing. Depending on rear axle ratio this has a variety of speeds. Mine is a max tow with 3.42 gears... I believe the difference in 3.42 and the 3.08 is so drastic that I will never own another 3.08 anything. The 3.42 is ok to lock out in 5th gear Tow haul active also. This disables AFM also so no back and forth. If on long stretch of road and your weight is low you can go 6th gear but the heat build up in the trans is bad for it so I suggest let it eat in 5th gear when towing. In major hills 4th will do you just fine, let the grade braking do some work for you also on downhill portions, it should keep you from burning up the brakes on your rig.
Trailer brake controller is key on downhills, a gust of wind or passing car can cause sway depending on your weight and the axle ratio of the trailer. Just ease on the trailer brake controller on the down hill portions if it ever gets a little tail happy. Don't ever stop of the tow vehicle brakes in that situation as it compounds it and makes things worse.
The shorter wheel base tahoe/yukon/escalade is a very capable tow rig when done right. As others mentioned the short WB makes it prone to sway on a larger trailer. Travel trailers normally do weight distribution hitches, just do not do too much on the hitch as without tongue weight the trailer will be more prone to sway. The sway control systems/ bar do help, but a properly setup trailer hitch, tongue weight etc is more effective than any bar you add. Remember to always have the front of the trailer about 1-2" above the rear of the trailer, this makes it track straight.
If you have air suspension and MRC it will help things out, if you don't, I would suggest helper bags in the rear coil springs for towing heavy for added suspension handling.
Towing with a short wheel base does have a great benefit when it comes to maneuvering and backing up.
Another aspect, Max air pressure in the rear tires when towing heavy loads helps keep the rear end planted and more in control.
Keep up with maintenance on the tow rig... fluids, tires etc and she will do you just fine.
Sorry for the long response, just figured alot of things need to be covered to tow safely and secure. I've been pulling trailers for 30 years and have seen so much wrong over those years.