There are numerous threads on PPR about x-wind take-offs. Essentially you get airborne with 'crossed controls' - in this example, right rudder and left aileron. These controls are restored to neutral in a 'cordinated' smooth fashion at and after rotate. At lift-off the a/c starts to drift downwind, being no longer constrained by the runway surface, BUT it naturally 'weathercocks' into the relative 'wind' (slightly left of the nose) by yawing to the left and 'fine tuning' then takes place to track the centreline with no yaw or roll present. That's how it should be done - then, of course, there's my thrashing about of the controls
