How to monitor my children's text messages

There is no app for that. There is another thread discussing this question. The only answer that has surfaced is to tell the child not to delete text messages, and that if they do they lose the phone for a period of time.

If the phone shares an Apple ID you can set it up to mirror imessages on another iOS device or a Mac computer. But this means that they will see your messages also.

Set up messages in iCloud in Settings, so you receive everyone in your family's texts, or refer to Lawrence Finch's idea.