A lot of how a vehicle tows has to do with having the trailer set up properly. You want to tow level and keep the heavy parts of the trailer inward toward the trailer's center. Obviously, you want the weight forward biased, but not with excessive tongue weight. In some cases a weight distributing hitch is called for to move weight to the front wheels. A bigger tow vehicle will be more tolerant of a bad trailer set up, but a minivan will tow 3500 pounds well if properly set up.
A healthy 3.8 should have had enough power. Probably half of all vehicles are running around with a 3/4 plugged air filter - that's fine on FI engines if you are just putting around town - throw a load behind any vehicle, and head up into the mountains with a plugged air filter, yep, it will be disappointing. Even with a perfectly maintained FI engine, you are also at a disadvantage w/o a turbo or supercharger at elevation.
Because of the available space, people often forget how much of a load (easily 1,000#+) people often have inside a minivan, before a trailer is hooked up. In that respect, a lot of minivans are running around with more of a load than many pickup trucks.
I'm with you downslope that I prefer a RWD frame based truck for towing. But, for many people that does not make for a good daily driver.
All this has reminded me of one more thing..... OP, assuming that you are getting an automatic in a new vehicle, seriously consider getting something like a Scangauge II to monitor Transmission temperature - that device will do a lot more than just Trans temp, but IMO it is worth the price just for that task. If what you get next has a 3500# towing rating, I'd also vote for getting a load-distributing hitch.
Rgds, D.