It's hard to tell from that photo if that's a paint
job gone bad, or issues with the original gelcoat. In either case, the first step is probably to remove and see what you've got going on with the substrate, after which you can forumulate a plan for repair (I can't imagine that you won't end up taking it all off anyway, but you could do just a representative area first to see what's going on and to test your removal method(s)). Sanding, scraping, stripper... it all depends on what's really going on there. I'd probably start with some sandpaper, and then work from there.
Gelcoat and paint
It's true that you can re-gelcoat something fiberglass once it's out of the mold, but there's typically little reason to in this day and age of two-part LPU paints, such as Awlgrip or Alexseal (to name two specific brands), which I would consider superior in a later application (indeed, some high-quality boat manufacturers are now simply painting
straight away and skipping gelcoat altogether).
Gelcoat is in its element when you can spray it into a female mold, which is what you do when you're molding up something like one of our trailers. After that you lay in the reinforcements and resin, let it set up, and then remove the mold (or the item from the mold, depending on how the mold is set up). Voila.
Spraying it on later... well, you can... but there's not really any benefit to doing it later. It's not really being used in its best element then, if that makes sense. Gelcoat can be sprayed, but it's not really how it works best. If you've done the necessary prep, and you have the access to (or are paying someone for) professional spraying equipment, then why not put on a two-part linear polyurethane paint? (My opinion here.)
I know that when I first got into boatwork, I had that feeling that "Oh, I want gelcoat! Paint is a later coating, and must be inferior." Now paint CAN be an inferior coating, and like any finish, the prep work is directly related to the final outcome, but it's no longer something that is necessarily slapped on later and is not as "strong" as original gelcoat (assuming using something like a two-part LPU in a sprayed application). A paint job like this can still be hard and shiny more than 20 years later.
Of course there are lots of paint applications that have the "put on with a broom" look, which is probably why people think "Ewww" when it comes to paint. There aren't that many "home-broomed" gelcoat jobs, so you don't see those, and many people are probably comparing the "home broom" paint job to the "professional" gelcoat job, and thus not seeing the amazing paint jobs that are done now. After all, no-one gelcoats their car when they make it into a street rod