Make sure your mouse is set to control the ship as well (in other words, set your mouse axes to movement axes in the settings). You will then be able to steer the ship with both your mouse and your joystick at the same time (pull left on the joystick and right on the mouse for example, for some funny effects).
As long as the mouse is set to steer the ship, you can see the dot. The dot is actually a seeing aid for the mouse arrow which appears when you use the mouse for steering. You should be able to leave the mouse alone in some corner so that it does not impact your flying, or set the deadzone for the mouse axes to maximum, at which point it will not steer.
I also have the mouse set for viewing, so when I unlock the mouse look, the dot disappears but I can pan around the cockpit.