100% you should pay but having given them money at this point you will not get that back. I would not give them a dime and tell them to get out, now! But if they are licensed they may file a lien so I would keep accurate records and photos of all conversations and work in progress.

Sorry this is happening to you. Here's what I recommend.

Hire a certified tile professional to come and do an inspection and give you a written report detailing everything that was done wrong and what it will cost to fix
it. (Ask them to do a flood test and anything they need to do to evaluate the waterproofing).

Here are 2 organizations with search tools on their websites.

www.tile-assn.com

Click on “find a contractor” and enter your zip code. Let the miles radius be fairly large, like 50 miles or so. The excellent tile pro that built all my bathrooms was on that site in my area, but about 40 miles away bc he was near downtown and I’m in a suburb.

www.ceramictilefoundation.org

This site has lots of good information on it. I didn’t find my contractor on this site, but a lot of people have told me that they had luck with it.

Here’s where you click to find a contractor:

www.ceramictilefoundation.org/find-certified-tile-installers

Also, if you are a nerd like me and you like to read, you could download a digital version of the TCNA handbook. It’s less than $40. It’s over 600 pages, but you don’t have to read the whole thing. Read the introduction (about 50 pages) and then read the shower chapters. You can skip all the other chapters such as swimming pools, etc. Reading this helped me to learn about the process and industry standards for water proofing and tile installation; it helped me to ask more informed questions, and helped a lot in my meeting with the contractor who messed up my shower.

www.tcnatile.com/products-and-services/publications.html

After the pro you hire for the inspection gives you his written report of all the things done wrong, have a business meeting with the contractor at the worksite and discuss all the problems. If it needs to be completely redone, ask them to do that, at their expense. They will either agree, in which case you give them a chance to redo it, or they will refuse, in which case they are effectively quitting. Confirm with them that if they don’t attempt to redo it, they are basically quitting; get them to acknowledge that fact. After the meeting follow up with an email documenting that conversation, and asking for acknowledgement, so that in the future they can’t claim that you illegally fired them. In that email, say something like “We were so disappointed that you decided to quit the project rather than
fix the [ list of problems ]. Because we have to have the shower rebuilt, we are requesting a refund in the amount of [$$$] in order for us to hire a new contractor and for the purchase of replacement materials.” They will probably respond to that email to refuse you the refund, but at least then you have an electronic paper trail that shows that you did not fire them illegally, that they quit instead. You can then go to small claims or district court to sue them if you want, but that’s a real PITA.

In the scenario where they agree to redo it, give them a chance. When/if they mess it up again (and maybe have the inspector come out a second time), then you can legally fire them in most states. That’s how it is in TX where I am. If you want to know for sure you can look up your states statues online and read the construction laws. If you aren't sure and you don't want to read the laws, assume that you have to give them a chance to fix first before firing them.

Sorry this is happening to you. It happened to me. It's far too common.

thanks so much for the advice and information!