If a mother is at the airport, ready to board a plane to go overseas, can the father enforce an ex parte interdict if she was not yet served with papers?
Bear in mind that the father in question is out on bail for alleged sexual offences and is under an order by the court not to see or contact the children. They were never married and there is no court order stating that he has parental responsibilities.
Even if he could get an interim ex parte interdict - would rule nisi apply if the mother was already at the airport through security?
Divorce / Separation Lawyer
The intent of your question is confusing. You really need to discuss this with an attorney in person. Rules nisi are rarely invoked and not for the reason you imply in the few facts you have presented. You have asked about whether the mother can leave. But you discuss children. Far too complex for a simple Q&A forum. However, if there has been no determination of parentage, then the putative father generally has no standing to prevent the children's international travel. Go see a lawyer immediately!