I ownd Honda Pilot with same drivetrain engine /transmission. I pull a Casita 17SD and while the Honda engine is capable the transmission is not. The tranny was constantly searching for the proper gear and that is while towing in D3. The transmisson fluid required changing after towing in the mountains ( due to overheating). Honda transimission must be flushed because you can only drain three quarts leaving a majority of the overheated fluid in the tranny. Flushing is an expensive service. Installing the Honda/Vue recommended towing equipement ( trans cooler - pwr steer cooler and wiring and class iii recvr) will cost over a thousand dollars. Buy a vehicle with a factory tow package - save money and have a better tug to start.
I installed a U-Haul
transmission cooler myself. It was relatively easy, taking a total of 90 minutes from the time I jacked up the Element to do the installation to the time I was taking her out for a test run.
Total cost: $50 for the trans cooler and a quart of Honda transmission fluid.
I've towed at my capacity (1,500 lbs) for two years now on some steep grades through the mountains and haven't had any problem at all.