My question involves a child custody case from the State of: Colorado

My wife and I are planning a family vacation to Madrid, Spain next summer to visit her best friend. We have a blended family and my 10yr old mentioned the trip to her mom and was told she can not go because she is too young. Since my daughter is 10 her mom has to fill out a form and have it notarized in order for me to obtain a passport for her. Is there anything we can do in order to obtain a passport so that we can take this vacation? If she still says no, is this something that can be brought to court? We also share custody of our 16 year old who does not need her moms consent to obtain a passport. Thanks