The charge line from the tow vehicle is small wire and it might recharge the battery (might) after a full day of driving. So don't depend on that method if you want to idle the engine for a half hour or so; instead, like others said, use jumper cables between the batteries.
I have a 75W solar panel and a controller, about $120. I wired it up to a 7 pin receptacle just like on the back of the vehicle. That way I can set the panel out in the sun and plug in the trailer's pigtail to it. This keeps my battery charged pretty well.
Batteries don't like to be discharged below 50%, which is 12.2V. Take a multimeter with you on your camping trip and check the battery voltage periodically (Harbor Freight has some for under $10). That way you can make sure you don't damage your battery.
