I can't unlink my Youtube account from my Google account. My issue is that when my teen logs in as me so I can monitor his usage, he then has access to all my emails in Gmail, which I would rather he didn't. Is there a way to ensure that when he logs into Youtube, he doesn't automatically get access to my emails?
No there isn't allow to use your account to access Youtube but to block access to another Google service.
The alternative is to use different account and to signout of your the account before sharing your device or to used your device multiple-user access features.