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!