Your unit likley has an EDPM membrane. It is a rubber like compound, but resists sunlight damage and should last the life of the trailer.
The downside is that any chemical with petrolium will degrade the membrane.
Dicor is likely the company that built the membrane.
If it is coming up from the substrate more than just a bit around the edges, it might not have been glued down properly. Dicor, the company that likely made it, makes an installation kit that comes with the proper adhesive, and sealant. It would probably require removing the gutters, vents, and edging to take the roof up, and reglue it. That would give you a chance to replace any rotted wood, and to let everything dry.
If the membrane is pretty well glued down, it may just be a matter of cleaning it up and removing all the old sealant, and resealing. Dicor makes special cleaner, and also special self leveling lap sealant.
On Dicor's site, it says Mineral Spirits dampened on a cloth can be used to remove stains that won't come off with the cleaner, but do NOT use Acetone (in caps on their site) or anything else with any amount of petrolium byproduct.
On mine, a couple years ago some cracks started showing up in the sealant, so it took most of a day to carefully pick that off without lifting the membrane off the roof. I found wiping the area with mineral spirit seemed to make the new sealant grip better, and I resealed with Dicor sealant.
Other than that, twice a year I wash the roof with Full Timer's Choice EDPM cleaner and treatment, and that seems to greatly reduce the chalky residue and black stuff. While I'm up there I always inspect the sealant.
I'd be hesitant to put some sort of liquid roof on there. Generally they don't look very good, and I doubt they would tolerate the flexing that RV's do without cracking.
Edit: I see this is your first post here. Welcome to the forum. You might also ask around other RV owners in your area. Maybe you are fortunate enough (like I am) to have a very capable and reasonably priced RV repair place nearby...
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