How do I get my iPhone text messages to stop showing up on my wife's MacBook Pro?

Not that I have anything to hide of course 😁

My wife and I have shared an iTunes account for years. Now that it is tied to an Apple ID, we share that too. Of course the problem them becomes since we both have iPhones, the Apple ID is linked to 2 phone numbers. This has not been a problem on our phones, as I found in the settings where I delete her phone number from the Messages program and she deletes mine. But she got a new MacBook Pro last week...and it is displaying text message associated with both of our phones. So she sees both her own conversations and mine. I haven't been able to find in the settings where I can remove my phone number from the messaging program on her MacBook Pro. Is there a way to stop this from happening?

She's also wondering if there's a way to only show the messages on her MacBook Pro when she's logged on to it. She's been frustated that if she hasn't been on all day, when she logs on all the texts she's sent/received will show as new messages even though she's already read them on her iPhone. I presume that the only way to stop that is to disable the messages app altogether, if that's even possible?

Thanks!