Create "virtual" display for use with remote desktop
You could use the Session Select feature of Apple Screen Sharing service.
It allows you to log in into a "virtual" user session without showing anything on physical screen.
To do so you should:


create second user account and log him in "physically",
connect using Screen Sharing to your iMac with your PRIMARY user credentials,
Screen Sharing will provide you with 2 choices: "Share" screen with current physical user or "Log In" in a "virtual" session,
select "Log In" and here you are: you have a "virtual" screen not visible to current physical user.
You can now change screen resolution to match your MacBook's screen.