The ability to make decisions regarding treatment of a minor child depends on which parent has legal custody of the child. In cases where the parents have joint legal custody, they each have the right to make decisions (just as they did when they were together prior to the divorce).
Physical custody alone does not necessarily determine legal custody.
Normally, parents will have joint legal custody unless one of them has been denied visitation with the child (in which case the denied parent would normally not have joint custody for purposes of deciding on dental care).
The only way to be absolutely certain regarding the parent’s respective rights and authority is to request the parent bringing the child to the office also bring copies of all documents relating to custody and medical expenses of the child (e.g., divorce decree, separate custody decree or agreement, document referencing child care expenses or insurance coverage).
It may be uncomfortable to ask for documents – but not as uncomfortable as dealing with an angry parent who is claiming you acted improperly by taking instructions from the wrong person when you provided treatment.