dentist getting overpaid and doesn’t want to give me refund

Basically I got braces at somos dental they charged me 3700$ for it. Year of 2024 I had a contract with them saying braces were billed 3700$ insurance willing to pay 1300$ leaving me to pay 2400$ for braces. Payed them off right, year of 2025 some how my insurance plan changed to HMO(😭😭) and basically my insurance stopped giving out payments of those 1300$ they accepted to give. Alright that happens, leaving at insurance only paying 704$ and my new balance that I own now is 2995$

I get a new insurance , and it’s ppo now in year of 2026. I have payed 2600$ for the braces leaving me to own 300$ only. The lady the administrator who handles all billing I guess was kind of enough to say, “I’m going to send out a claim to see if your new insurance can pay that balance!” I’m like okay? I later find out she sent out a whole new claim as orthodontic treatment of braces and my insurance accepted to pay 1800$… leading to overpayment now right? And isn’t that upcoding right too? So now, I’m like alright then since they have 1800 over with just a balance of 300$ they should give me 1500$ back right. Well I speak to her she would tell me yeah we will fix this, it’s just that we don’t know how your insurance will send us the 1800$ it can be payments or direct check. I’m like okay understandable, I called my insurance they said oh yeah we actually sent the WHOLE amount not by payments. I’m like oh shit really okay I told her, proceeded to say okay I just need to wait for the check to come to our billing department and we will forward that refund to you, ( keep in mind we haven’t talked about the numbers of that refund) but me thinking they have logic they would know. 2 weeks come , I speak to her about it she’s like okay you’re getting 700$ back I’m like why? She said PPO or HMO gave us nothing so basically your contract was 3700$ , um no so I called my old insurance they confirmed they gave 704, went back to the office proved her wrong and now she’s saying that she can’t issue me a refund from my insurance claim I’m like well it’s not from my insurance claim it’s from my overpayment. But yeah honestly I don’t know what to do now. Am I wrong or they wrong