Re: refinish bath enclosure
First have you tried cleaning it with a product for removing water stains like CLR or one of the others. Although there may be soap scum build up on it the stains are more likely lime, rust, or other deposits from the water.
You say it looks like Corian. Without knowing for sure I would be reluctant to sand because it could be a product with a very thin veneer and sanding may remove the veneer completely. Besides sanding you would probably have to polish it restore it.
Be sure you live your life, because you are a long time dead.-Scottish Proverb