First you have to be concerned about tongue weight and how it may affect your tow vehicle, the TT and towability.
To isolate the battery you would need to build a partition in the box to keep everything away from the battery. Keep in mind batteries do emit fumes that can be toxic as well as explosive so you need to vent the tool box. An option would be to mount a plastic battery box in the tool box and run venting hoses from the battery box to the outside of the tool box.
I carried the kind of stuff you're writing about in my tow vehicle in a wooden box I built.