Hello Amy and welcome to TFP!

When exactly was the pool installed? At first impressions, I have to say what your installers is doing seems like a foul in my opinion. Builders have an inherent responsibility for proper grading/leveling, stability, and plumbing/shell installation. That's just basic pool procedures. Can a pool settle over time? ...... of course. But there is typically a warranty period for things like that, and yours sounds incredibly short. Because the skimmer is typically surrounded by concrete or some other type of decking material, it's a bit more work to remove a skimmer, followed by the re-plumbing, and I suspect they are trying to get out of that work. Seems a bit sketchy.
I would keep working with the installer to make it right, not just for the skimmer, but I'd be worried about what else wasn't completed properly that they should be responsible for. Having said all of that, if you no longer have a good relationship with the installer, or simply wish to move on and not have them over anymore, a cracked skimmer can sometimes be repaired depending on the location of the crack(s). So I would recommend posting a pic or two of the skimmer and the problem area. We'll see what we can advise based on those pics.