I had a similar situation, where a contractor (my pool guy) ruined my plaster with an acid wash and refused to replace the plaster. I sent him a certified letter demanding the fix, and because, like you, I really didn't want that guy to "fix it" (and cause even more problems), I was hoping he'd refuse. I gave him two weeks, which is kinda key, and once he didn't perform, I was free to hire another contractor. That contractor replaced the plaster (full chip out) and did a great job. I later filed a complaint on the 1st contractor with my state's Contractors License Board. There's much more to this story, which I wrote about at length here at TFP, but the conclusion was: the Board stepped in and somehow forced the contractor to pay for the repairs. I was prepared to go to court, and that first letter, along with the two weeks to perform, would probably have worked out in my favor. But the Board did their thing and I was able to avoid court.
Point being, you may have recourse, and you may have a way to get everything fixed, by a better contractor, and make the 1st contractor pay. If you want more details about how to research this possibility, let me know...