The vinyl covering is Ensolite. It's closed cell foam with a bonded vinyl surface layer, and it's actually a very effective and durable shell lining. The lining has a number of important functions, including control of sound and
light (raw
fiberglass is translucent), insulation, and condensation prevention. If you remove it, you will want to put something back in its place, which is a fairly major project.
What many do is to clean the Ensolite thoroughly, remove the old T-molding, secure any loose sections, fill seams and voids with paintable caulk (a wet sponge can be used to approximate the original texture), prime and
paint.
If you do decide to replace it, a common alternative consists of a layer of foil bubble insulation covered with marine headliner. That's what
Scamp has used since the mid-80's. To do it right, you really need to R&R all the interior cabinets and
windows.
I recommend cleaning it as best you can and use it for a while before you decide how far you want to go with your
renovation. More than one have gutted a newly-purchased trailer only to find it is more time and money than expected.
Welcome and congratulations! I wish you the best getting this new-to-you trailer fixed up! How about some pictures?