Update: The two children received their passports in the mail today! Still waiting for one adult passport but we know it is on the way because we received the birth certificates separately in the mail with a note saying the passport has been sent.
It took a little over 2 months from the time we sent the forms in until the time the passports were in our possession (we did not have a travel date on the form for these passports)
For the daughter that needed hers earlier she was able to pick it up about 2 weeks before her travel date (she sent it in about a month and a half before her travel date). (We had the travel date on the form for this passport and she was asked to provide the documentation to prove she had travel plans, she just sent her flight confirmation information)
It seems to be a very long process as there are no real updates to know when they will arrive but in the end it seemed to have all worked out.
It took a little over 2 months from the time we sent the forms in until the time the passports were in our possession (we did not have a travel date on the form for these passports)
For the daughter that needed hers earlier she was able to pick it up about 2 weeks before her travel date (she sent it in about a month and a half before her travel date). (We had the travel date on the form for this passport and she was asked to provide the documentation to prove she had travel plans, she just sent her flight confirmation information)
It seems to be a very long process as there are no real updates to know when they will arrive but in the end it seemed to have all worked out.