Yes if you are entitled to claim the children. Assuming that you mean minor children that lived with you more then half the year and you meet all of the other requirements to claim the dependents.
Amended returns can only be mailed. It is suggested that it be mailed certified with return receipt (or other tracking service) to verify that the IRS receives it.
You can check the status of the amended return here, but allow 3 weeks after mailing.