Depending on the decor you (both?) choose should help guide you in your decision on whether or not you should replace or refinish the tub. Hopefully, if you choose to keep it, you can get it out the doorway or you'll be stuck refinishing it in the bathroom, or cutting it in half if you decide to replace it!
Anyway, before you get too far, buy yourself (and your husband) a book for less than $30 on Bathroom Remodeling. (This is less costly than having to hire a plumber to correct anything you break or forget to do!) Amazon.com and FatBrain.com Books are just 2 on-line book stores that you can search for bathroom remodeling. Of course, there are Border's Books, Lauriat's, Barns and Nobels, etc., etc., on the outside (as well as probably on-line too) that have these books on the shelf. Reader's Digest and Time-Life Books publish them for sure, among others. I found an on-line reading-walk-through you (both) can do to see what you're in for. It's put out by HomeTime Projects. Click the Getting Started URL, do some reading, then at the bottom of the page, you can go onto the NEXT phase. And so on.
As for the last item you inquire about, I know it as Liquid Floor Leveler. Read the instructions before you buy because it may not be suited for your situation. There is a maximum 'thickness' for leveling, if I'm not mistaken (like 1/2" or 3/4" max???) Well, read the can. If your 'correction' is more than the max, you have a new project.