Can I use this construction to mean "Know better than to do something"?
You know not to interrupt when someone else is talking.
=
You know better than to interrupt when someone else is talking.
Or does the first structure not exist?
One way of expressing this idea:
You know that is it rude to interrupt when someone is talking.
You can leave out words without changing the meaning this way:
You know not to interrupt when someone is talking.
Therefore I believe the first example sentence is acceptable, and the second example sentence is also.
"Know better" is a shorthand phrase that is understood to mean "You know you should not (do an action)..." by using the phrasing "You know better than to (do an action)."