You should consult with an attorney to prepare. Motion asking the court to prevent such behavior
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You might want to start by documenting your concern in writing to your ex and asking that he be more considerate of the children. If that fails and you want relief from the court you must file a Motion. Within such a Motion the court can offer some relief, i.e. that the step-father is permitted to attend events and/or pick up - drop off, etc...
Kenneth A. White, Esq.
New Jersey Family Law Attorney
The Answer provided was based on the limited information provided, and represents information based on the law in general, not a legal opinion that can be relied upon. Before a formal legal opinion can be offered I would need an opportunity to review all possible relevant facts and circumstances. You cannot rely on the advice of an attorney given over the internet. The exact facts of your sitaution, including facts which you have not mentioned in your question, may completely change the opinion that is being offered. Please be aware that the above comments are neither protected by attorney-client privilege, nor may the same be the basis for a malpractice lawsuit.
The court would probably first order you two to mediation to discuss the issues, then therapy if that didn't resolve it. Yes, dad needs to accept that there is a step-parent involved, and he cannot legally stop you from authorizing him from having a role in the child's life (e.g., picking up the child, attending medical appointments, meeting with teachers, etc).
You wouldn't add verbiage to your MSA, you'd get a post-judgment order clarifying it and enjoining him from interfering. My suggestion would be to handle this gently; dad may be feeling threatened about his role as a parent (actually, this more often seems to occur with women when a step-mom becomes involved but, as here, it goes both ways). Dad needs to be reassured that he's the only dad the kids will have, but also needs to accept that they also have a step parent. Having more people in a child's life who love him/her shouldn't ever turn out to be a negative for a child.
IF YOU LIKE THIS ANSWER AND APPRECIATE THE TIME IT TOOK TO WRITE IT, PLEASE SELECT IT AS "BEST ANSWER." Thanks. The above is said without seeing your case file and without my understanding the entirety of the facts of your case. Depending on those facts, the above information be may incomplete or may be completely inaccurate. The above is intended as general information only based on what you described and not as legal advice. I advise you to consult with counsel who may be able to provide better information commensurate with a better understanding of your situation.
My colleagues are correct in suggesting you would need to file a motion with the Court regarding the current circumstances. You say, however, that your former spouse uses the Agreement to prohibit certain actions by your current husband; the language of your Agreement is relevant and without review of that language, your next steps may not be clear. You should consult with an attorney familiar with family law to help discuss the particulars of your case and give you advice as to the most likely outcome and work with you to develop a plan to move forward.
The information presented in this answer is for informational purposes only. The answer or the information contained within should, in no way, be construed to be formal legal advice nor the formation of a lawyer/client relationship.