How can I stop wife from leaving the country without my consent with the kids?

You have to file and Emergency Petition for Custody of the children ASAP.   Are you in the process of separating or divorce proceedings?  Do you have an attorney?  The attorney will know how to file this.  If you do not have an attorney then I would suggest you hire one as soon as possible. If you do not think that you will gain custody then file a Petition to enjoin her from leaving the country and turning over their passports to the court for safekeeping until the matter an be worked out.  If she violates the order then she could be guilty of kidnapping.

I am going to assume that Illinos is the "home state" of the child.  Below is an explanation of how the Illinois Courts dterminse that they have the right to hear the custody case.

The Uniform Child Custody Jurisdiction and Enforcement Act (UCCJEA) is the law which tells Illinois courts whether they have the jurisdiction to make a child custody decision.  Jurisdiction is the ability/authority of a court to hear and decide a case. Illinois courts do not have the authority to hear a child custody case unless they have jurisdiction, or the authority under the law, to make a decision. The purpose of this law is to prevent disputes between states over which states' courts can decide a custody case and to stop courts in two different states from making decisions in the same custody case.

Under what circumstances can Illinois courts hear and decide a custody case?

The UCCJEA makes so-called home state jurisdiction the priority basis in which a court has the authority to hear and decide a child custody case. Illinois would have home state jurisdiction in the following circumstances:

• Illinois is the home state of the child on the date that the petition for custody is filed; or
• The child is not in Illinois, but Illinois was the child's home state within six months before the petition was filed, and a parent or person acting as a parent is living in Illinois.

Under the UCCJEA, "home state" means the state in which the child has lived with a parent for six consecutive months previous to the custody action being filed in court. If a child is less than six months old, the home state is the same in which the child lived from birth with a parent.

Good luck.