This answer may not satisfy you, but I am obliged to explain what the law "is" and "is not" -- even though the law may not be to your liking.
Insurance is designed to reimburse the insured (you) for health care services. Typically, the insurer pays the service provider, because it takes the burden off of the insurered, who does not have to pay the service provider up front, and then wait for reimbursement from the insurer.
In your case, the insurer has reimbursed you for the dental services received, because the dentist returned your insurance proceeds to you. The insurer is now relieved of having to pay the amount that it has already paid -- otherwise, you would receive insurance reimbursement in exchange for no services rendered.
You can return your 50% reimbursement to the insurer, who would then be obligated to pay your new claim to Dentist B, but as long as you retain the payment from Dentist A, you are obligated to pay out that 50% to cover your costs. And, since your plan is apparently a 50/50 plan, you are also liable for the other 50% -- which is 100% of the Dentist B claim.
Now, if it turns out that Dentist B's bill is larger than Dentist A's, then you would be entitled to additional reimbursement from the insurer to cover 50% of those additional costs, above the amount that you paid to Dentist A, and which you now have received.
But, for example, if you had a credit card bill that had other charges, and Dentist A's repayment has covered those charges, then you have been relieved of a corresponding debt that you no longer have to pay. From an accounting standpoint, you are no worse off than you would have been had the money been returned to you in cash.
BotXXXXX XXXXXne, you cannot recover from Dentist A, and you are fully responsible to Dentist B for the amount originally paid to Dentist A. If there are additional charges, then you would have a new claim for 50% of those Dentist B charges.
Note: If for some reason the insurer refuses to pay the additional Dentist B charges, then you may be able to sue Dentist A for the wrongfully directed refund, because then you would be able to show an economic injury to you based on Dentist A's actions. But, unless and until the insurer refuses to pay any additional Dentist B charges, you have not suffered any economic injury, and without an "injury in fact," you cannot sue anyone -- because that is the fundamental rule of law -- the plaintiff must suffer an injury to have standing to sue.
I hope that my explanation makes it possible for you to understand and deal effectively with the result of these transaction with the Dentists and the insurer. I wish I could give you an answer that would force Dentist A to return your money to the insurer. But, I can't -- at least not unless and until you can show that you have suffered an economic injury related to Dentist A's actions.
Please let me know if I can clarify or further assist you.
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