I can't say for sure if you can or can not use fiberglass repair kit,
The fiberglass resin is a styrene resin. Should be compatible with your tub.
You can get "whisker" reinforced resin that has shredded fiberglass mixed into the resin in order to help strengthen it.
1. clean up hole to get to solid material all around.
2. sand it down well to remove any soap residue, clear coating, etc. and make the surface ready to accept the new resin. It will be bonding to the surface, rather than chemically linking with the rest of the material. Make it rough so it has lots of places to grab hold.
3. fit a patch over the back side and fill in the hole with resin. If you are using filled resin, I would say leave it a little shallow, then top it off with unfilled resin so you don't run the chance of having whiskers of fiberglass sticking through. Also tint the resin to color match your tub.
4. sand smooth 200, 400, 600, 800, 1000, .... use automotive type wet sanding paper.
5. Finally clear coat to seal it up and make it shiny.
Wear a dust mask and use LOTS of ventillation. The uncured resin is not pleasant stuff to be breathing.
Something tells me that replacing the tub wouldn't be a whole lot more of a PITA