Honesty is the best policy. Why would a married person not include especially their children or any other pertinent information on the application for that matter? It only complicate things. Now here it is, this person has a spouse and 2 children that really need her and they cannot not join her because of dishonesty/selfishness!!! If your family is important to you, you should either surrender your green card or go back home and spend a lot of time with them as this situation cannot be reversed. How sad and unfortunate.
Therefore, I advise everyone to be honest in ALL of your dealings, come what may!