You need to go into the monitor properties and select the extended desktop option for monitor 2 not clone.
Actually I think that you may already be set up for that from what you have said
The first time that you use an extended desktop it can be a little confusing.
Open a program or a webpage on the laptops screen then drag it over to the other monitor with the mouse, depending on the way its configured the second monitor either left or right. It sounds like your primary monitor is the laptops so it will have the extra one as the secondary off to the right, even if it is physically to the left of the laptop. Most people will place the second monitor to the right in your setup to save confusion.
Once the window is on the second monitor it operates independantly of monitor 1 and will work as usual on monitor 2