Thanks for ALL your suggestions which are well appreciated but most of which may not be applicable.
However, I believe the below is applicable in my case.
First, I will need to apply for my own naturalisation first to get the citizenship. Then the following may apply to the kids afterwards.
Children of U.S. Citizens Residing Outside the United States
Children residing outside of the United States may obtain citizenship under Section 322 of the INA. A child who regularly resides outside of the United States is eligible for naturalization if all of the following conditions have been met:
The child has at least one parent, including an adoptive parent, who is a U.S. citizen by birth or through naturalization;
The child’s U.S. citizen parent or U.S. citizen grandparent meets certain physical presence requirements in the United States or an outlying possession;
The child is under 18 years of age;
The child is residing outside of the United States in the legal and physical custody of the U.S. citizen parent, or of a person who does not object to the application if the U.S. citizen parent is deceased; and
The child is lawfully admitted, physically present, and maintaining a lawful status in the United States at the time the application is approved and the time of naturalization.
https://www.uscis.gov/policy-manual/volume-12-part-h-chapter-5