father has mental illness
Family Law Attorney
It would be a very bad idea for you to do that without the father's consent or a court order permitting you to do so. The father could file a writ to have the children returned to the United States, you could be arrested, and the children could be placed with the father. If you go to a country that is a member of the Hague Convention, they are under a duty to do what is necessary to have the children returned to their home country.
If you are serious about moving to another country with the children, do it the right way and save yourself a potentially big problem.