Your narrative is not clear to me, but to the extent I understand, the dentist could be liable on a range of claims, including possibly breach of contract and fraud. Specific performance is the claim that might force him to do the work, but why would you want him to do it.
I don't understand yournrecitation of facts and question posed. Try repost in a more coherent statement otherwise younwill not get any answers do to the confusion you created.
My answer is not intended to be giving legal advice and this topic can be a complex area where the advice of a licensed attorney in your State should be obtained.