Trailer park in California. It's a prefab kit built accessory room. The main part of the trailer is normal, just this accessory room is built out of aluminum panels (about 3' x 9' per panel) and then plenty of single pane windows.
Mold growth is a moisture problem which can either be because of condensation or because of leaks. I agree with the contractors, properly framing out and insulating the interior would probably help a lot with condensation on the inside of the aluminum, as would double pane windows. Ventilation is also important for stopping mold growth.
Or it could just hide the mold behind the insulation if done poorly. In cold weather, when cavity insulation, the inner surface of the metal will be cold. If warm, humid interior air that can sneak behind the insulation and get to that surface, it will condense. And metal is impermeable to moisture, so it can’t dry to the exterior.
One technique to mitigate this that does not require extraordinary care on the part of the installer is “flash and batt”: apply a thin layer of spray foam to the exterior wall and then fill the cavity with fiberglass, mineral wool or some other fluffy insulation. The spray foam adheres to the wall and leaves no space for humid air to reach, and the inner surface of the spray foam will stay warm enough to avoid condensation.
One issue with flash-and-batt is that it’s absolutely not a DIY project: the equipment is specialized and expensive, and you need to take real precautions to protect yourself from the unreacted chemicals. But you might be able to get a local spray foam contractor to do it for a few hundred dollars if you ask nicely and let them come by on their schedule when they’re already doing a job nearby.
Frame first — you want the foam to stick to the exterior shell and to the framing members that are up against the exterior. Protect anything you don’t want foamed — the fresh foam sticks to everything and foam in your electrical boxes is no fun.
(The unreacted chemicals are not persistent — they’re too reactive to stick around.)