how can i read my child's text messages on my iphone or computer

The general answer is you can't read someone else's text messages regardless of your relationship to them. If you share an Apple ID (which in general is a bad idea) you can set their phone to forward messages to your phone, then lock the settings in Settings/Screen Time. But it would be hard to set this up without them knowing. And you have to do it carefully, so they can't see your text messages.

The next problem is there are many 3rd party messaging products. If they can install any of these (WhatsApp, Facebook Messenger, Signal, Symphony, Google Duo, Telegram) there is no way to intercept the messages, so you would have to block installing apps on the phone also.

If you are willing to let them know you are monitoring then there are other options, such as automatic backups that you can then view.

On your phone go to Settings/Messages - Text Message Forwarding and turn off her phone. In Send & Receive on your phone, make sure only your phone number is checked.

On her phone set Text Message Forwarding to your phone. Then in Settings/Screen Time - Content & Privacy Restrictions - Allow Changes disable Passcode Changes (so she can't lock you out of her phone). Unfortunately, there is no way to prevent her from unchecking the forwarding to your phone if she knows to do that.

So Plan B is to go to Settings/<your name>/iCloud and turn on iCloud Backup. Then make sure her phone is plugged in overnight; this will create a new backup, which you can view with an app like https://iphonebackupextractor.com.

Note that there is no perfect solution, other than viewing her messages on her phone (which she clearly has to cooperate with).