Change the location of MyLocationButton in GoogleMaps

Well first of all the Action Bar is now deprecated! Stay on trend and use the toolbar! Toolbar is supported in Android OS since 2.2

Here is a good example for you https://examples.javacodegeeks.com/android/android-toolbar-example/

Secondly, you will have to implement your own button with location detection.

Here is one of the options for implementing the button - determining the location:

private LatLng fromPosition;

FAB = (FloatingActionButton) findViewById(R.id.imageButton);
    FAB.setOnClickListener(new View.OnClickListener() {
        @Override
        public void onClick(View v) {
            cameraFromPosition();    
        }
    });
    private void cameraFromPosition() {
        CameraPosition cameraPosition = new CameraPosition.Builder()
                .target(fromPosition)      
                .zoom(17)                   
                .bearing(180)                
                .tilt(80)                  
                .build(); 
        map.animateCamera(CameraUpdateFactory.newCameraPosition(cameraPosition));
}

What is FAB and how to work with it: http://www.androidhive.info/2015/12/android-material-design-floating-action-button/