I've removed two fridges. One came out easily after I found all the attach points. The other needed a bit of persuasion. It should slide out, from the front, with a bit of wiggling back and forth. One had a sheet metal casing around it, with additional screws, the other didn't.
Make sure all 12 volt and 110 power wires are removed. Also make sure it is disconnected from the copper gas line so that it can be moved.
Some trailers did have the cabinets fibreglassed to the shell with no rivets being used while other trailers were rivited. This was probably a cost-saving technique. You can probably cut your closet out and then fibreglass it back it later. Without seeing your particular Boler
I am guessing that a sawzall would work to remove the closet.
If you are painting
the trailer then it is pretty easy to patch all old rivet holes with bondo/ bondo hair or bondo glass. There really isn't too much you can wreck on the Boler. I've put holes where I didn't need them and have moved other holes around. The repair is a quick fibreglass chop patch, a layer of bondo, proper sanding and feathering and then prime and paint