If you want to be technical about it, the violation is actually your child's, for failing to go through immigration properly (not sure what that crime is called). As a parent, you presumably could be charged at least as an accessory to that crime, although your child likely would not be charged if they are particularly young. Having been implicated as an accessory, your GE privileges could be revoked.

I don't think there is anything on the GE website to suggest that bringing your child through with you is not a problem. True, as noted, others have reported some unofficial flexibility in the past with respect to minor children, but that's the extent of it.