I have a Durango and yes, the payload is your biggest issue. With girls, you're unlikely to see the growth spurt that turns a 50lb squirt into a 130lb refrigerator, but you need to factor in additional stuff as they get older and bringing friends along.
You also don't mention how many girls you have.
With my SLT, I would not tow anything more than about 4500gvwr even though it says "6000 towing capacity". And I don't have the additional people and their stuff to bring with me.
Another thing to note is that if you are looking at the lightweight trailers, some of them have well less than 100lbs available for stuff in them (some only have 200-300 lbs available), so once you fill the fresh water tank, there's no available "weight" left in the trailer for stuff so you can reduce weight in the tow vehicle.