I highly doubt that your horse is giving a true half pass. If she's half passing, she will have a good understanding of collection, leg to hand, be very loose and supple, and find leg yield a walk in the park. There is a reason why half pass is not introduced in tests until medium (3rd? US) level.
Leg yield is one of the first movements we teach a green horse, to begin an understanding of lateral work.
Leg yield itself is NOT a lateral movement, as it does not involve bend.
A good leg yield involves the horse moving forward and sideways according to the riders aids. It's body remains straight and upright (shoulders should not be dropping in either direction), with the poll and jaw flexed slightly against the direction of travel. The rider keeps a firm outside rein, and rides their inside leg towards this outside rein. The outside rein controls the outside shoulder, and the inside rein assists gently in maintaining the flexion. The inside hind passes infront of the outside hind, and the inside fore passes in front of the outside fore.
The rider should be sitting lightly over their inside seat bone, inside leg at the girth, outside leg slightly behind. Hips and shoulders should be straight, or VERY slightly angled towards the direction of travel.
In a green horse learning leg yield for the first time, only ask for a step of two at a time. I tend to start on a circle, as most horses tend to find it easier to understand the sideways movement when you already have a basic inside leg-outside rein established on the curve. On a straight line, they also tend to just walk straight towards the edge of the arena, rather than sideways.
Bring your outside rein out towards the outside shoulder - this creates an 'open door' for the horse to move into. Eventually we will close this door to form a direct outside rein, but in the learning stages, we just want to encourage the horse to step into this space. Apply your inside leg, and as soon as you feel the horse step sideways, ride forward and straight again. In Dressage, quality is ALWAYS more important than quantitiy. So it is much better to do two or three good steps, than 20 unbalanced 'sort of sideways' steps.