I'm not familiar with fiberglass bathtub problems, but we had a fiberglass shower that developed a hole where it was unsupported below. My coworker put a bag of sand (no hard edges and it would sit there nicely) underneath the hole for support, and then he sanded down an area around the split, resurfaced the small area, and painted it good as new.
Essentially, that is how they repair boat hulls too, when they get defects in them.
I would say you do not need to remove the tub, most of the time fiberglass repair is a quickly done job. (Think about those lovely Corvettes having fender benders and getting fixed good as new.)
Can you contact the tub manufacturer? It might be they will tell you who to call in to make repairs. Or, like the above poster indicated, you could go for a long time with no leaks and continue to use your tub.
Q