Interior lights can be wired directly to the battery in your trailer to run independently of the vehicle. You'll just want an in-line fuse/switch like # 37212515 to cut the power when not in use.
You can charge the trailer battery with your vehicle's battery by installing a charger like the Redarc In-Vehicle BCDC Battery Charger # 331-BCDC1225D. This DC-to-DC battery charger draws power from your vehicle to provide power to an auxiliary battery on your trailer or RV and has a solar option... view full answer...