Do I need to take my battery home to trickle charge?

Trailer will discharge the battery flat dead in a week or so if you just leave it.
If you disconnect a battery cable it will sit just fine for 2 to 4 months.
If concerned about security you could place the battery in the trailer while you are away or just bring it home.

If you have sun on the trailer 100 watts of solar on the roof should keep you charged indefinitely.


On edit:
Actually if the trailer never moves you probably do not even need a battery.