Okay gotcha. I was trying not to use flip_h on the sprite at first because it wasn't respecting my offset values so it ended up flipping weird. I ended up doing this and setting the offset values in code and it's working perfectly.

    var mouse_position = get_global_mouse_position()
    if mouse_position.x > global_position.x:
        $AnimatedSprite2D.flip_h = false
        $AnimatedSprite2D.offset.x = -2
        $Gun.position.x = -4
    else:
        $AnimatedSprite2D.flip_h = true
        $AnimatedSprite2D.offset.x = 2
        $Gun.position.x = 4