I don't want my former spouse to take my child out of the country!

Child Custody and Visitation: Can the court order my spouse to visit with the child in the United States and not take the child to a foreign country?
The short answer is the court can do whatever the court wants. But as a general rule, the court will not restrict visitation to the United States, or locally, to New York without evidence that a parent is likely to “kidnap” the child and not otherwise adhere to the visitation order.
In a case where the non-custodial parent has a history of violating the visitation order, the court might require the non-custodial parent to post bond before taking the child out of the state or country. In that situation, the non-custodial parent would put a sum of money into an escrow account as insurance that he or she will bring the child back. Once the child is returned, the parent would get the money back.
If the child is taken to another state within the United States and retained illegally, the problem is a lot easier to handle than if the child is taken and retained to a foreign country. These types of disputes are governed by federal laws – The Uniform Child Custody Jurisdiction and Enforcement Act (UCCJEA) and international laws pursuant to the Hague Convention.
If the parent does kidnap the child and takes the child to a foreign country, then hopefully the country is one that is a member of the Hague Convention – an international treaty between member nations to protect children from abduction and retention in a foreign country. However if the child is taken to a country that is not a member of the Hague Convention, the custodial parent could be out of luck.
These countries are members of the Hague. The list may not be all inclusive:
Albania, Argentina, Australia, Austria, Belarus, Belgium, Bosnia, Brazil, Bulgaria, Canada, Chile, China, Croatia, Cyprus, Czech Republic, Denmark, Ecuador, Estonia, Finland, France, Georgia, Germany, Greece, Hungary, Iceland, Ireland, Israel, Italy, Latvia, Lithuana, Luxembourg, Malta, Mexico, Monaco, Montenegro, Netherlands, New Zealand, Norway, Panama, Paraguay, Peru, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, South Africa , Spain, Sri Lanka, Sweden, Switzerland, Turkey, Ukraine, United Kingdom, United States, Uruguay and Venezuela
The court would definitely look to the relationship between the parties, and the character of the parents in making a determination of whether to restrict visitation. But the court cannot restrict visitation without a good cause. Taking the child to a country that is not a member of the Hague might be good cause under certain circumstances. Otherwise the decision is likely to be over-ruled by the appellate court.