I am not sure I fully understand your question.
Do you believe that you were Involuntarily Denied Boarding (what is commonly called "bumped") solely because you have two children? That seems odd.
Airlines are required to file with the U.S. Department of Transportation their Denied Boarding Priority list (see link below). These lists are also available for you to read on the airline's website typically in the section marked "Conditions of Carriage."
GENERALLY SPEAKING, the lower you are on the list, the higher your chances are of getting IDB'd. Typically the lists blend two categories, the fare class and category (discount fare passengers get bumped before full fare passengers, coach goes before first class) and status in the airline's frequent flier program (the more you've flown, and the more miles you have, the better chance you have of staying).
Keep in mind that airlines typically only bump people when they cannot get volunteers to take a later flight. And bumping rules must be applied without discriminating based on membership in a "protected class" (e.g. race, religion, etc.)