The only solution I have found to this is to right click the ribbon above the right hand screen and select the sketch tool bar from the drop down list. The sketch tools then appear down the right hand side of the screen and can be dragged up to the top. When sketching you then have a duplicate set of icons on the right hand screen. This can be done for Features and assembly tools also.
By default, that top toolbar (called the CommandManager) is docked in the SOLIDWORKS window, so if you move your SOLIDWORKS window, it should move with it. If you have undocked the CommandManager, then it won't move with the main window and you have to manually move it by just dragging it (by the tabs or other empty space). If you want the SOLIDWORKS window on one monitor, but the CommandManager on another, just drag it to the other monitor using the tabs or empty space of the CommandManager. If you are looking for something else, please clarify.
I hope this helps,