If a parent is refusing to sign a passport application, the other parent can apply to the courts to waive the requirement for Passport Canada to receive a passport application signed by both parties. However, this will be an expensive process and if a trip is already planned then due to the slow nature of the courts it may be nearly impossible to obtain the passport in time.
Children over the age of 16 can apply for their own passports, so this may be a solution in certain situations.