After working for a home improvement company for many years & seeing practically everything under the sun that customers have done before we had to go in & redo/do over/tear out, I would suggest that you replace the tub surround. Absolutely do not sand. There is a nasty smelling chemical sort of like paint thinner which is used to prepare such a surface before applying the stuff bobad gave the link to. The epoxy stuff can be remarkably horrid-bubbling up, scratches easily (It does not like real hot water) & then it is impossible to remove once it starts turning into a mess.
If the tub surround looks that bad, you might try closing your eyes in the shower.