Family share child is receiving my texts messages

Apple IDs are personal; they shouldn’t be shared any more than you would share a toothbrush. If you share an Apple ID with someone else many bad things will happen. Each user should have their own Apple ID, then you can create Family Sharing→What is Family Sharing? - Apple Support. That way you can share what you want to share and not share what you don’t want to share.

It is OK to share an Apple ID among devices used by one person, such as an iPhone, an iPad and a Mac; in fact, it is a very useful thing to do. But not between devices used by different people.

Here is Apple’s FAQ: https://appleid.apple.com/faq/#!&page=faq. See the 4th bullet item.

On the 2nd phone go to Settings, tap on your name, then scroll down and tap sign out. Or, on your phone, go to Settings, tap on your name, then tap on the other phone listed at the bottom and delete it from the account.

The child must be logged in to the same Apple ID that you are in Settings/Messages, unless they also share your Apple ID for other things.

Open Settings and look at the name at the top. Is it different on yours and your child’s phones?

Next go to Settings/Messages and tap on Send & Receive on both devices. Are any of the email addresses duplicated? What about the Apple ID at the bottom.