Plugging into your running tow vehicle will generally not charge very quickly; by the time the current gets through all the (fairly small) wires and connectors between the alternator and the trailer battery, you have enough impedance that you'll only get a slow charge. A better option to use the tow vehicle alternator would be decent jumper cables between the tow vehicle and the trailer battery more directly.
An even better option, as mentioned, is a relatively modest solar setup if you'll be camping in a reasonably open area.