Wow, what a nightmare you are experiencing. It is such a shame how you pay for a pool, and then trying to get repairs done are next to impossible. I just had a repair done from my pool company, which, in turn, made the original problem worse. I called and called and emailed pictures as well, to no avail. NO return phone calls or emails for weeks. I finally had enough, and left a voicemail, as the person I needed to speak with was never available when I called. I told her on the voicemail that I would send Five On Your Side out to their store to do a segment on poor customer service and pool repairs gone bad. Five On Your Side is a local segment where a local news channel sends a reporter into the field to investigate situations where people have paid money and not gotten what they paid for and can't get what they want, a refund, or fix the original faulty repair etc. Well, I DID get a call that night! They didn't want those cameras in their store and on the news causing all that bad publicity, and the owner was at my house 2 days later!
So, if you have a news channel that has that service, I would try to threaten them with that as well. Lawyers will definitely scare the pool company, but cameras, and reporters invading your business is something NO company wants to deal with. WAY too much bad publicity for any company, and it will usually get their attention to follow through immediately.

Good luck with your situation.