Q: Is there a way to sync Imessage on a minor's Iphone 5 with Mom's Iphone 6 (iOS 9.1 on both)?

No you can't sync your phones for imessage app.

What you can do is use the same apple id for imessage - settings - imessage - send & receive - enter apple id.

this will give you access to your minors sent and received imessage, as well as your minor being able to view your sent and received imessage.

There is no way for you to monitor it short of you taking the phone and looking at their message.

Link your iPhone number and Apple ID to use iMessage and FaceTime - Apple Support