I've considered replacing but the size/opening we have is not standard so there would be some framing changes and we'd need to hire a plumber...

You’ll get a much better result by replacing. “Refinishing ” is just painting it, and it will peel.

If it’s acrylic, it’s a standard size. Remember there’s a difference in the rough opening to the studs than the interior finished size. Do you have an access panel behind where the valves are located?

It won’t help with the discoloration but try deep cleaning and then apply a coat of ‘gel gloss’. See if that makes it look nice enough for your purposes.

Waste of money for no good reason (unless it's pink or aqua or avocado). Leave it as is and try cleaning the floor better (carefully) and polishing it. Put a bold shower curtain on it and call it a day.

Painting that thing--pro or not--is a temporary hack. He'll have to destroy the current top coat in order to put on a temporary color. So you'll have a ruined shower with a delicate paint job.

If you just cannot live with it, replace it; it can't be any more that the paint job.

NO is the answer .There are enclosures that can be trimmed to fit .

Thanks everyone for the feedback. I think I'll pass on the re-coating!