You cannot affirmatively apply for cancellation of removal. You would have to be in removal proceedings and present your case before an Immigration Judge. Given the facts you laid out my answer is an unequivocal "no". If you are not currently in proceedings it's simply a risk you absolutely should not take.
You cannot apply for cancellation of removal unless you are in removal proceedings. You should consult with an experienced immigration attorney.
The answer provided here is general in nature and does not take into account other factors that may need to be reviewed for a more precise answer. You should consult with an immigration attorney before taking any action. The answer here is not intended to create an attorney-client relationship.
To place yourself in removal proceedings is a very serious situation. However, your window of opportunity is not unlimted. As a family, you should discuss with a very competent immigration lawyer and make that decision.
Mr. Murphy is correct, you can't 'ask' to file for cancellation.
Mr. West is also correct ... getting yourself put into removal proceedings is the LAST thing you should think about. Wait 7 years and have your 14 year old sponsor you.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship.