I'm going to reiterate what what @malba2366 said- its THE POOL BUILDER'S insurance company that needs to be hit up for this, not the pool owners!
If he's licensed he has to carry liability insurance, right?
If the Home Owner Insurance wants to cover it and then subrogate to the Pool Builder and his insurance let them do it. That way you get covered and repaired regardless of what the PB will pay. And the HO insurance handles negotiating/fighting with the PB and insurance. They are much more experienced at recovering for damages then you are.
Off the cuff I'd say we're looking at a $40k plus damage claim. I think most homeowners policies would cover this sort of thing had the homeowner done it. However, as Maddie pointed out, this is not the fault of the homeowner, it is the fault of the contractor. The homeowner's insurance will insist on the contractor being liable. I am not sure if homeowner's insurance has an "uninsured contractor" clause like an auto policy might. Like I said, lawyer up. I would not wait for that part. If this was me, I would have a cease all work order with the contractor, get an expert or 2 pool builders in to assess the damage, contact my homeowner's insurance for guidance, and take it from there.
Under no circumstances would I allow that contractor to even attempt to remedy that repair.
You probably have to give the contractor the right to inspect and remedy the defect, and you have to give reasonable notice to do such before filing a claim. I would notify him of the defect in a certified mail letter and email so that you can have documentation incase you have to file a lawsuit. You should absolutely get an opinion from another respectable contractor to see what a proper repair would entail. If the original contractor refuses to perform a proper repair (ie. not fill it with water and hope it settles back) then you unfortunately have to get a lawyer involved. Homeowners insurance may cover accidental damage caused by a contractor, but they will not cover damages resulting from negligance on the part of a contractor.
My $.02 on insurance. I'd talk to your agent to see what they advise. If you're not satisfied talk to an attorney experienced in contract law, not to sue but to get his/her advice on how to proceed. Insurance rules vary by state. It's hard to tell what insurance company is liable and if multiple actually what's your most favorable route without reading and understanding the policy. I've had issues unrelated to pools with my previous construction management life. Even if you read the policies yourself it's hard to figure out what they mean sometimes. It may be difficult (not impossible) to file a claim on the contractor's policy if you didn't get a "named insured certificate" prior to signing with him. It could be best to have your insurer "battle it out with them" or not. When you need professional advice it's good to pay a couple hundred dollars for it. This is one of those times in my opinion. Also, lawsuit is last resort in my experience. It will take years to settle and even then you may have a judgement that is difficult to collect.