Not to tell you how to suck eggs but is there a VIN number plate on the trailer? If not, do you have any registration paperwork? The VIN should be on there. Otherwise, there's probably no way to get the actual VIN.
For the make and model, there's a good chance that it came from a trailer manufacturer who's still around, such as EZ Loader or Loadmaster. You might trying contacting them to see if they have a record of what models they built for S2 Yachts.
Are you trying to register the trailer? When I bought my boat the VIN plate for the trailer was gone. The trailer had also been modified. So I registered it as a home-built.