Can I get a J1 waiver if I have US citizen children?

Its not enough to have U. S. Citizen Children and a U. S. Citizen Spouse. You must prove that the U. S. Citizen will 'suffer extreme hardship' as a result of the two year residency, as a matter of both discretion and law to the satisfaction of the State Department and USCIS. Otherwise, your child and wife must decide whether to stay in the U. S. or accompany you for the next two years in your home country. If you are unsuccessful, you may be banned from an immigrant visa for ten years if you remain in the U. S. while the J-1 visa waiver is pending. Good luck. The above is general information, not legal advice, and does not create an attorney client relationship. I strongly recommend an appointment or teleconference with a competent and experienced immigration attorney before the decision to file a J-1 waiver is undertaken. Good luck.