iPhone 4S: how to set up multiple phone numbers under text messages send/receive option
This question covers the procedure you will follow to re-enroll your children's phone numbers under your new Apple ID. 

On their two phones, go to settings app, tap iMessage and sign out of e old account. Sign in on your account and set their "Caller ID" for sending iMessage to be their phone number. Repeat for any/all devices that use your new Apple ID.

However, there are problems with this approach.  Just be aware that when you get your children's messages, you only get their iMessages (message sent from an Apple computer or an iOS device only). SMS from non-Apple phones still go directly to their phone without you seeing them. 

Your children will receive a copy of all of your iMessages as well and they could send messages as you (but not your SMS).