Mirror modifier creates an object inside another. I need a Mirror modifier to correctly create mirrored object. How to fix this?
You can mirror around a different object. For example if you select the headphone band as the mirror object it will use that to mirror around instead of the origin of your object. If there is nothing handy to mirror around create an empty and put it in the midpoint of where you want to mirror. In your case I would imagine the headphone band would work for you as the mirror object.
The easiest thing to do is to make sure your model is centered on the y and x axes (OBJECT>SET ORIGIN>SET ORIGIN TO GEOMETRY) and then hit "N" and in Location make sure everything is "O" zeroed out. Then position one ear piece, in the object menu select set origin to 3D cursor (which should also be centered (Shift+C). Then mirror X will work perfectly.