Command sponsorship has been pretty painless so far. My husband went to his levi brief and filled out a bunch of paperwork. I had to sign a few and then turn it in. The passports were pretty easy, we filled out the application online and then just printed them out for our no-fee passport. We needed our birth certificates, SS cards and the form. We got them back in 4 weeks.
Then EFMP was an online questionnaire for each child, asking developmental questions and a quick interview to verify all medical and education needs, and done!
Then after a little complications on our side needing a paper signed we finally got a confirmation number that we had been put in for command sponsorship, got our tracking number and the website to track it on, and all in all we knew we were approved a week after everything was submitted! Easy Peasy!
Next on the schedule, my husband put in for early report, so he had to fill out his leave form for PCSing to reflect us leaving at the earliest point possible. His orders say that he can report up to 60 days beforehand and since I'm pregnant, the earlier the better for my flying. His leave form was approved and now we're just waiting on orders!
I'll update more about Korea once we move. :)