I used a synthetic upholstery fabric to line the headliner on my boat..never had any mildew problems except where dirt came in through hatches. So I think the Hull Liner will work well. I used contact cement but 3M spray adhesive should work well. Usually this kind of fabric has a rubberized backing.
You can control mildew with Trisodium Phosphate. I would try a carpet cleaning machine (Steam cleaner) and put TSP into the solution container. We had a moldy spot on our living room rug that kept coming back until I treated it with TSP; no more problems. You need to control humidity in the trailer...not easy in some areas of the US