custody 问题请教各位

joint custody, Physical custody of child to father, child visitation granted to mother.

question: If father take child out of USA without mother's aggreement, not for vacational purpose. Is this criminal?
Both parents are GC holder, if the child doesn't have a passport. Is it true that both parent need to sign on the passport application form? In another way, is there anyway that father can legally get a passport for the child and take child out of USA w/o mother's signutre or agreement?

Many thanks to whoever reply.