Why are they saying you need a class III hitch? You stated you have a class II already. Isn't it rated for 3500 pounds trailer weight
You stated the trailer's gross weight
is 3000 and your van's towing capacity is 3500. The trailer is within your rating- it will work fine.
Some people might say "don't drive too fast" or "don't drive long distances" but as long as you are safety conscious and within your vehicle specs- no problem. You can tow an RV. Don't let anyone scare you off. Everyone here wants you to be safe for your sake and theirs, but you don't have to be paranoid when on a trip. After all, isn't it supposed to be a vacation? If you make sure you have your rig setup correctly (trailer brakes, tongue weight, not overloaded, etc) you should have many happy miles on the road.
One thing you will want to keep an eye on is the transmission fluid. Chrysler minivan transmissions (especially older 3.3L V-6 equipped 4-spd autos) were notorious for dying even when not towing. A transmission cooler added (if not already equipped) and regular servicing will help prolong the life of any auto, even Chryslers.
I hope this helps.
PS- A 5500 would be sweet! I'm jealous.