How can I read my child's text without them knowing it?
Are they an adult "child"? 18+ It seems like if they were a tween you'd just tell them you are the parent and would have made it a stipulation that you get to see the phone whenever and for whatever reason. Perhaps just having a conversation about your concerns of what's on it might be a good place to start vs. spying.
Without getting the device and looking at it, there are so many ways the child can exchange messages, you will have a false sense of control if you do figure out the way to spy on text messages. Search google for Verizon Messages app.