I really can't speak of tubs when it comes to vinyl and acrylic bathtubs. Acrylic Liners are about 1/4" in thickness, and the color goes all the way through it. (DO ask to be sure, or look for it to be 'documented' somewhere.) Be aware that this liner may come in 'pieces'. (I don't know for sure.) You may have added expenses, like needing to have the drain replaced because it's too old to work with. Or maybe now you want sliding doors.
As for vinyl bathtubs, do you mean fiberglass? If so, I have a shower stall that's fiberglass. In a lot of cases, it can be repaired if it gets damaged. Deep cuts are another matter BUT they're popular.
All that aside, my tubs are cast with a factory baked-on glaze. To have that re-done wouldn't last very long since the 'conditions' in my bathroom can't be matched by the factory conditions (where the glaze was originally baked on; not painted on.) So, in short, a liner would be 'better' than reglazing. I'd DEFINITELY forget reglazing.
As for removing the bathtub, it can be cut into pieces to be removed. HOWEVER, you'd have to find out if a replacement bathtub can be installed with no more than, possibly, having to remove the bathroom door (if you know what I mean. Obviously, you can't cut your new tub and then have it put back together!) If you're talking to a Salesman that's selling fiberglass and acrylic lines, I think you ought to talk to a Retailer that sells the traditional glazed bathtubs. Maybe they can send someone to your home to 'measure' things up. Maybe they can tell you what they can do to get a NEW, factory-glazed tub into the bathroom. (THey're pretty imaginative folks.)
If you have any more ?'s, e-mail me directly as your Post is getting 'buried' on the Forum. My best to ya and hope this helps.