IIRC, those sinks in the 2000s Classic line have some Corian and around the sink, I can't recall but I think it's a very unusual install, unlike the newer units made today that have what I would consider a normal under sink install.
I am not familiar with that coating that is on that sink, but if it is alum or cast, perhaps it can be refinished similar to a bathtub. If it's pure plasticy type, perhaps a epoxy type paint. I say that because the sink setups in those trailers I seem to recall being a bit different. Putting a stainless over that thin Corain if I am recalling correctly won't hold it, perhaps under, but then you might run the risk of breaking that thin section of Corain. My memory isn't what it used to be, but I do recall the Corian counter being fairly thick, EXCEPT around where it meets the under counter installed sink. Do you have pics of the sink area in your unit you can share?