1. If the account is in the child's name, that would be a violation of federal law. It doesn't matter that you're the parent - you can't spy on someone else's phone.
2. If their accounts are in your name, you can't read their texts any more than you can listen in on their calls - texts are transient, and appear on the two phones involved. I guess you'll just have to make it a rule that they have to give you their phones for inspection. (And any "kid" young enough to be spied on is too young to be walking around with a cell phone.)