My wife has a 2011 Town and Country, 3.6 liter. I don't see it as a vehicle suited for towing a trailer that will be pushing 4000 lbs ready to go camping. Maybe a popup but, a travel trailer's going to add a lot of wind resistance to the weight you're already pulling. We pull a 5700 lb dry weight trailer with a Suburban 1500, 5.3, SumoSupersprings. The wet weight is probably 6500-ish. It does OK. The chassis is fine. The 5.3 works pretty hard on the up hill pulls. Personally, I think you will be really unhappy trying to pull a travel trailer with a 5th generation Chrysler/Dodge minivan. Don't get me wrong, we love the vans we have owned. For what they are built to do they are awesome. But, IMO not built for pulling a travel trailer. For years we pulled a 16 foot, single axle Prowler TT with an F-150, a Jeep Grand Wagoneer (V8) and a Toyota Landcruiser FJ60. The F-150 did a good job of towing. The Jeep and the Toyota sucked. Based on that experience I wouldn't consider towing any travel trailer with the minivan. Also, based on what I have read about the transmission in those vans I think towing that kind of wind resistance and weight will be hard on it.
We had a class A gasser motorhome. We decided we wanted to go a different direction so we bought a new 27 foot TT. I used the cash that I got from the sale of the old motorhome and bought a Suburban (as a third vehicle). I found mine at a small used car lot near my house. Mechanically it was very sound but needed some TLC. I did a few jobs to bring it up to as perfect as it could be (parking brakes, transmission filter, new speakers, all oils and fluids, differential rebuilt). At the time my toad was a Honda CRV. Since then I sold the CRV and just drive the Suburban as my daily driver. Point is, we wanted the travel trailer and made it work within budget. With everything I spent to get the burb up to speed I was still under fair market value.
Don't believe what the salesman tells you about what can tow what. They want the sale. In 2012 Chrysler went with bigger brakes on those vans but, they still aren't intended to stop that much weight even with the brake controller. You're going to need a weight distribution hitch which will add like 80 pounds to the hitch weight. The rear suspension's going to be well over what it was built to handle. And, there's not much that's affordable to fix it. I have been under there and seen exactly what those suspensions look like. I recently replaced the shocks on our T&C. The suspension bumpers are inside of the springs. Pretty major surgery to boost up that rear end, even if the rear wheel bearings can handle it over the long haul, which I have reservations about.
You would enjoy the travel trailer for sure. But, I can tell you that towing with a vehicle that can't do the job very well takes all of the fun out of it. Once you load up the van with stuff and wife and kids. Then load up the trailer with LP gas, water, clothes, food, lawn chairs, TV, spare tire, bicycles and plastic forks you're pretty heavy, even with 17 feet. Most 17 footers have a single axle so, weight and balance can be funky if you're not really paying attention. We found that crosswinds could be pretty terrifying on top of a tall bridge crossing the intracoastal waterway.
That's my 2 cents anyway.