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Yes, certainly you can draft a custodial agreement as between yourselves and then go file such with the court to make if of record.
Yes, if your fearful that she might attempt to leave the country or even the county where you both now reside - most definitely get a custodial order in effect and have it signed by a judge. Then, if she attempts to leave, she will be in contempt of court. However, she could always ask the court for permission to relocate - then it would be the court's decision but only after you've been given an opportunity to argue against such.