I've pulled our popup with an 03 Honda Odyssey for probably 20,000 miles of the van's 211,000 total miles. All original powertrain. It's not 1992 anymore, folks.
No way I'd consider pulling a full height RV trailer with a minivan though. No. way.
You can and will be very successful pulling a 12 foot, LOW wall popup without slide-our or front trunk and carefully set up the van to tow. That means:
1. A Reese 350mini (or 400 single bar)weight distributing hitch. Specially made for popup sized trailers. Fixes rear squat and loss of front wheel traction.
2. Custom installation of an electric brake controller on the van. Preferably a P3 or Prodigy model by Tekonsha.
3. Change trans fluid by the SEVERE service interval in the manual.
4. Verify you have the factory tow package or if not install an auxiliary ATF cooler on the van.
5. Pack LIGHT. No full water tank, no bikes, no firewood, no bowling ball collection. Food, clothes and stuff you'd take tent camping in your Civic. No more. Be ruthless. Less is more anyways.
My recommendation is a Jayco 1207 or a used Fleetwood Sun Valley. Sleep the biggest kid on the couch and the other 4 on the king bed end. Mom and Dad get the other bunk end. Tight, but sure beats tenting! Awning screen room attachment advisable for more bug resistant elbow room.
You don't need more stuff to entertain you. The destination is the entertainment!