I have only removed the "sponge liner" in a few places for fiberglassing in cleats to mount additional shelves.
But I can assure you it would be a big job. Mine is apparently glued on with either a construction adhesive or a contact cement. Whatever it was, it is really glued down good.
If you were to replace it with something like carpeting, then it would be a lot easier because the residue could be left. But if you wanted to prepare it for
painting, all the residue would need to be removed down to bare fiberglass. Once this was done it would require a lot of filling and sanding.
Years ago we had a Compact Jr. that was painted inside from the factory. The fiberglass lay-up on this trailer was quite nicely done in fiberglass roving. A spackle paint of white with brown flecks was originally applied. I cleaned it up well and applied a new coat of latex enamel. This went on nice and looked great. The problem was sweating due to no insulation.
Concerning the mildew smell -- I would bet the plywood floor is the main culprit. Another prime possibility is the cushions. The mildew that gets on the ceiling is mostly a cosmetic problem. I did as a previous poster, cleaned well, then used a mildew resistant paint as an undercoat, overcoated with a white floor enamel.