First off, courts are not bound by child custody and child support provisions of separation agreements. Judges do whatever they want with these issues.
The best course of action is to secure the consent of the other parent in advance of the child receiving medical or dental care. If this is not possible - for whatever reason - get your child the care he or she needs and worry about the legalities later.
A party’s actions can always be “held against them” in court, just as that party’s actions may work in his or her favor. If your agreement is incorporated and one party is violating its provisions, you can go the show cause/contempt route. If it’s unincorporated and you want to do something about the situation, you’ll need to ask the court to set custody. You’ll be given the opportunity to describe all the bad stuff the other side has done, including violating the terms of the agreement. The judge will listen to what both sides have to say, and then render a decision which, in all likelihood, neither side will like very much.