Thank you. However, I was told I cannot submit N-600 since I haven't lived in US for 5 years. Is this correct?
That requirement is only for a particular situation, i.e. if you are their only USC parent, and you're claiming they acquired US citizenship when born abroad. See
http://travel.state.gov/law/citizenship/citizenship_5199.html
But now you're not claiming their US citizenship at birth, you're claiming they derived US citizenship after birth by obtaining green cards and satisfying the other conditions of the Child Citizenship Act of 2000, which has no years of residence requirement for them or you.
You'll have to provide the following evidence for their US passport applications:
1. Proof that you're they're parent (their birth certificates with your name on it). If you're their father and married to their mother, you also need the marriage certificate. If you're not married to their mother, it gets more complicated but I figure you already know those complications if they obtained green cards through you.
2. Their green cards.
3. Proof of your US citizenship -- either your US passport or Consular Report of Birth Abroad or N-600
4. Marriage certificate, or divorce/separation papers showing you have with legal custody
5. Proof that they're physically living with you -- for example, medical or preschool records showing the same address as you
Note that if you apply for the passports first, you'll have to provide the above stack of evidence again for the N-600, and they'll take away key documents like your US passport or Birth Abroad certificate for the duration of the passport process.
But if you get their N-600 approved first, you won't need to send the big stack of documents again when applying for their passports; the N-600 certificate by itself will be enough to prove their US citizenship to obtain their US passports. And the N-600 doesn't require you to submit any original documents during the process; you'll send copies with the application, then bring the originals on the day you go to pick up the certificate.
So with those facts in mind, given that they're so young that they probably won't need any proof of US citizenship anytime soon, if you're going to apply for both you may find it more convenient to get their N-600 first (even though people typically apply for their kids' US passport first because it's cheaper and quicker than the N-600).
