I think this borderline, but it could work. A lot depends on how heavy you load the minivan. The 3000 lb. figure with 5 passengers and luggage, does not take into account the variables with those 5 passengers or luggage weight. 2 small adults with 3 small children is different than 2 big adults with 3 teenagers. It could be 500 lbs. or 1000 lbs. Shame on Chrysler for being to vague.
If the minivan has a heavy duty tow package, it may already have (and should have) an auxiliary transmission cooler.
A light duty WDH would be a good idea. Make sure the factory hitch has the stats to handle the weight.
Terrain makes a big difference. An occasional trip into the mountains might be OK, but if that is the main travel area, then the minivan may not be a good choice for a TV. I pulled my 1000 lb. pop-up over the Blue Ridge here, and I was down to 2nd gear in my Jeep, doing about 25 miles per hour......it was embarrassing.
If you decide to go this route, I suggest you load up for camping with the family in tow, and get everything weighed, to see if you are within the limits of the Town and Country.