Insulation in the construction trailer, vapor barrier yes/no?

Insulating from the outside is unfortunately not really possible. Hmm, I wonder if that is allowed? No idea, but I really don't care. The car is on private property and only inhabited by me, if someone gets upset about that, I really don't know what is wrong with people. No one gets hurt anyway.

Insulating from the outside is unfortunately not really possible.
Hmm, is that allowed? No idea, but I honestly don't care much. The trailer is on private property and only occupied by me, if someone gets upset about it, I really don't know what's wrong with people. No one is harmed by it.

well, heating a construction trailer with a chimney in Germany...

that reminds me of quite a few stinkers

The internal insulation should be possible, provided the interior space is still large enough after insulation. However, and I mention this as a caution, the camper will become a thermal cabin. With polystyrene insulation, you really don't need a vapor barrier anymore. Polystyrene doesn't let anything through anyway, not even moisture. That means, with regular heating at outdoor temperatures below zero and little forced ventilation (windows open), mold will only be a matter of time. If it can't be helped because of the coal, I would install a stud wall construction (wooden beams, polystyrene in between, and as a finish towards the interior a gypsum board). Good luck.

I would choose PUR. Aluminum laminated. More expensive than Styrofoam, but better in terms of insulation. I would use a vapor barrier and apply it very carefully. The further construction is up to you. Don’t forget the ceiling and the floor. So wrap the whole thing all around. Pictures would be welcome. In any case, I find the project interesting.

Thank you for the answers,
There is already a wooden stud frame present. Basically, I wanted to build the wall exactly as you said, but on the inside there will be plywood because I find that visually more appealing.

I'll consider the PUR, it is just twice as expensive, so I have to see if my budget allows it. Apart from the better insulation, does PUR offer any other advantages?
Regarding the vapor barrier, I do assume that I will manage to make it completely airtight on the inside. However, I haven’t yet come up with anything useful on how to seal the space that forms between the sheet metal and the vapor barrier. I’m just worried that otherwise moisture will get into the gap from the outside.
About the pictures: I’m currently replacing rusted-through sheets and removing the roof felt from the roof (by the way, any tips on how to do this better than with brute force?). Afterwards, an EPDM roofing membrane will be glued onto the sheet metal roof.
Unfortunately, water has gotten into the vehicle in the past, so some of the battens (all oak, mh ) are pretty rotten and will be replaced.

Then immediately check if you can insulate the roof from the outside. Somehow. That is simpler in terms of construction.
Advantage of PUR: lower thickness, same effect as styrofoam. So more living space.
Then there is some space left for OSB3 boards inside. With that, you can completely line it. If you make it airtight, that also counts as a vapor barrier.
It must be airtight from the outside. Absolutely. If moisture penetrates from the outside, mold will come faster than you can blink.