When I applied for the kids' passports in August 2014, I had to submit their father's death certificate in lieu of his signature. Signature (possibly notarized; I vaguely remember her father's notarized sig being required when D21 applied for a passport at age 15) or certified proof of exception (no copies; the application processor will make the copy needed) will be required.
OP: When you say "your attorney", do you mean an attorney admitted to the bar of the state in which you were divorced, or a legal services firm which completes paperwork but does not represent you in court or provide specific advice to you?
Because, frankly, if that is the exact wording of the relevant section regarding legal and physical custody and < parenting time >, I am worried about how durable the order is to court challenge.
Could you please let us know the state? Passports are a federal issue (Hoosier's post covers the specific issue), but "disappeared" does not always equal "stays gone".