A little over a year ago we had our tub refinished. The job was not very good and the finish is starting to bubble up, crack, and peel away from the tub. I never really thought the tub needed refinishing but my husband did and so we refinished the tub. Is it possible to remove the new finish off the tub to reveal the original finish and just leave the tub as it is? I don't think whoever did the refinishing sanded the tub or prepped it for refinishing and that is why the finish is coming off. Any suggestions would be very helpful. I'm not really wanting to do a bath fitter or anything like that because they also have issues with water getting under the shell.

It's not like you don't have options. It's just none of them are very good.
1)You can remove the refinish by using some paint stripper and a let it on the surface long enough to do its job. If you have to work hard to remove the coating, put on more stripper and let it sit longer. Or you could take a window razor blade and scrape it off.
2) If the original finish is funky you can refinish or install a tub liner **or**
3) replace the tub
Good luck in whatever you decide, Tom