Trailer Truck

What truck should I use to pull a 35' travel trailer to avoid sway?

My Dad has a 35 foot long travel trailer and pulls it with a YukonXL. The trailer is 9600 lbs. fully loaded and maxes out the capabilities of the Yukon XL. The reason he went with the YukonXL was passenger capacity as there are usually 8 of us.
Ideally I would like to buy a truck that will fit 8 of us and pull the trailer with no problem. It does okay pulling the trailer but if we get up over 55mph or 90kph (depending on wind) the trailer can really start to sway. It's like the tail is wagging the dog. If no truck or modifications are available to assist with this then I guess we're stuck with it. If there is some way to correct this problem (different truck or some modification) I would like to know about it even if it means we can't fit all 8 of us in the truck. We are already using two anti-sway bars between the truck and the trailer.

Sorry to hear that. People correct me if I`m wrong. And I know a lot of you will. But is pulling a 5ton trailer behind a SUV that needs to have a full load, 8 people just to stay on the road, is that something you want to be on the road with?
But seriously, I would suggest you keep the Yukon to carry the people, Buy/get (and I`m gonna hear it from this) a Ford 450 super duty. Get something that is made to pull that much weight and still carry 5 people without wagging it`s tail, and probably pass the Yukon on the way.Yes I love my Dodge, but in real life, the Ford starts and stops consistently.Not faster or slower.just does what it was made to do. Work.!!! Another option is to sell the trailer and the Yukon and just get a big----- motor home. Enjoy your summer. Oh yes you don`t need a special license to drive this, but do think about how much weight you really have. take it to a public scale and get it weighed. You might be surprised to find out that your trailer is a lot heavier than what it says on the tags, and the load capacity on the truck does not include 8 people and a 5ton trailer.

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