The only way I have ever found to remove old caulking is to carefully cut it out with a SHARP razor knife. I own a Tajima 650 utility knife. Thsi thing is like an "Olfa" knife on steroids. It's really, really sharp and tough. I bought it a Sears for about $12. I find it most effective on this type of project.
On refinishing a fiberglass tub, sorry, I'll have to let someone else handle that one.