We've owned both a hybrid and a PUP. The '96 4Runner has a towing capacity of 5000#, the hybrid loaded to camp (water, food, clothes, etc.) was around 3300#. Well below the towing capacity but still, towing the hybrid wasn't necessarily a fun experience. It wasn't a power issue. It seemed like it was the tail wagging the dog sometimes. Plus, the wind resistance just ate gas. Our hybrid and our current PUP weighed the same and are of the same length. We got maybe 11 MPG average with the hybrid vs. 15 MPG with the 14' bed PUP (has a slide out, shower, furnace, etc.). After three or four years, we went back to a PUP and are so glad we did.
Remember that the weights shows are dry weights. No water, cooking gear, luggage, battery, propane, or furnace in many cases. A/C can add quite a bit to the trailer weight. Sure, you may have a 3500# tow rating, but that is calculated assuming a driver, not a bunch of passengers and gear. See if you can find the combined weight rating for the van, that will give you a much better idea of what you can actually handle.
Maybe if you're only planning short trips without much interstate travel a hybrid might work. But having had both with a very tow capable SUV, I'd recommend the PUP over the hybrid with your set up.