Can I play the same game on two different Xbox One consoles with only one Xbox Live Gold account?
Unfortunately, you cannot play on one Xbox Live on two Xbox One's simultaneously.
You can only sign in to one Xbox One or one Xbox 360 console at a time. If you try to sign in on a second console, you'll be asked whether you want to sign out from the first console. If you respond yes, your account will be immediately signed out of the first Xbox One console.
Xbox Support - Concurrent SignIn
You cannot play on 1 profile with 2 different xboxes at the same time, so you'll need 2 profiles with Gold.