my current thinking is this is some sort of oddity with iMessage using the same Apple ID on both devices.
Under normal circumstances, a message sent to an Apple ID would be broadcast to all devices using that same ID.
On your daughter's iPhone if you tap Settings > Messages > Receive At, do you see your Apple ID listed?
If so, you may wish to create a new Apple ID that your daughter can use for non-Store services.
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Please go here: https://appleid.apple.com/
Click "Create A New Apple ID"
Once you have created the new account, go to Settings > Messages > Receive At on your daughter's iPhone and remove your Apple ID. Then, add the new ID you just created.
Hopefully, this will result in the behavior you want/expect.