Please understand the vast majority of participants here, myself included, tow almost exclusively with heavy duty pickup trucks. Their opinions of smaller vehicle tow capabilities are tempered by what they currently use to tow. They will tell you WHAT THEY WOULD NOT DO, not necessarily what can/should not be done.
Does this Odyssey have the tow package on it now? Does it have a receiver hitch? If it doesn't have a receiver hitch it probably has nothing else for towing. Then you have to factor in the cost of adding all that equipment for just one trip.
If the documentation states the vehicle can tow 3500lbs, it can tow 3500lbs. In the passenger classes of vehicles they usually allow for adequate payload capacity to tow the rated amount, AND have the vehicle reasonably loaded with people and stuff. That is also probably with whatever towing equipment option package the manufacturer provides, but you can emulate that with aftermarket equipment.
