Does she require both signatures to get this? (it's my understanding she does for passport).
If the kid is under 13, yes she does require the father's signature. If the kid is 13 or over, only one parent's signature is required.
However, if the father is acting against the best interests of the child, the mother can go to the family court and ask the judge to waive the requirement for the father to sign. But I would think long and hard before doing anything which involved the family court.