What about a pop up? For an example,
CLICK HERE.The transmissions on the Dodge van should be fine. The issues were from the early 90's and the newer transmissions are fine, including the 4 speeds still in service (41TE transmission). I got 292,000 trouble free miles out of mine.
However, it's all about weight. The Grand caravan with the 3.6L V-6 has a towing capacity of 3600 pounds, a GVWR of about 5700 pounds and a vehicle weight of about 4500 pounds. The pop up I linked to has GVWR of 1500 pounds. So, being conservative, figuring a 200 pound tongue weight (spec says 170), that gives you room for about 1000 pounds of payload in the van. When you add the passengers and any gear into the van, that may be getting close, but I don't think you'd exceed it.
But, when you get into mountainous areas, you may find it struggling a bit. I'm sure others will add in more info and opinions, but if you really want a minivan I would suggest looking at a popup and consider that a good compromise between tent camping and a trailer. If you really want a small trailer, than the minivan is not viable, and I would be looking at some of the vehicles mentioned here or at a truck, again depending on what size trailer you're considering.