Harold, I have to wonder if something was seriously wrong with your van's drive train. I had better success back in the '80s, when I towed a 13' egg trailer (UHaul) 2,000 miles with an '84 Dodge Omni 2.2L 4-cyl. We went from MI to CO and back, no problems other than the fact that it had a hard time maintaining 55 mph on the freeway! :) No, I wouldn't do that again... but really, a V6 should do just fine with an egg trailer!
OP, the thing you must watch for is too much hitch weight. Trailer mfrs list DRY hitch weight, with no LP, battery, water, or gear. A minivan with a 350 lb hitch weight limit will require you, practically speaking, to buy a trailer with no more than 250 lb dry hitch weight.
Some minivans, such as the Sienna, are known to have a soft rear suspension that would make you wish for WD. Trouble is, you have to add the weight of the WD hitch onto your total hitch weight! The Andersen is about the lightest one out there, I think I read that it was 54 lbs but I could be wrong.
I towed for 140,000 miles (work and play) with a 2008 Highlander, 3.5L V6, 5000/500 tow rating. I replaced it with a V8 Lexus GX470, and I wish I had the HL back... but my wife didn't like the seat in the HL, so it is what it is. If you buy a HL, a Flex, an Explorer, or a Traverse, you won't have to worry about the hitch weight the way you will if you have a 350 lb limit. Checking your loaded hitch weight with a bathroom scale before every trip is possible, but tedious.
Or consider a 16' Scamp. They tend to be very light on the tongue, about 200-250 lbs when loaded.
