Your husband's adjustment of status is a little outside of normal processing times but enough to cause concern at this time. Your husband should consider seeking renewal of his employment authorization and advance parole document. There is no additional fee to renew these documents. He can file for renewal up to 120 days before expiration.
Your children will each need to file their applications for adjustment if status. CBP appears to be correct regarding your oldest child in the U.S. It does not appear your oldest is eligible for a K-2 visa based upon the information provided. The marriage had to occur prior to his 18th birthday before he would qualify. Unfortunately, embassies do make mistakes. There may be options available but more information is needed. I encourage you to consult an attorney ASAP. In the interim, you can read more about family immigration at http://myattorneyusa.com/family-immigration.
Answered on Dec 12th, 2016 at 3:46 AM