You are required to establish your residence in the United States for three years (is application for naturalization is based on your marriage to a U.S. Citizen) and during that time, have not left the United States at any one time for periods that exceed six months. It appears from the facts you presented that this is not a problem. Immigrations Services also require that you be present in the United States for the three months prior to your application for filing. There are exceptions relating to employment but you should consult an immigration attorney if it appears you have exceeded the six month rule, or have not been present during the three months prior to your petition for naturalization.
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Generally, a person applying for naturalization is not required to have his or her children present at the interview.
Disclaimer: the above answer should not be considered, and does not constitute, legal advice. You should not rely on this answer because each case is fact specific and could be subject to different local, state, and federal laws. My response does not create an attorney-client relationship between us.