Hi Martink,
Hope all is well.
So the main differences between playing across court and down the line is the slight adjustment in the feet position. When playing down the line you need to have the right foot (For right handed players) behind the left, and get more side on, this means the energy of the movement is going down the line more and not dragging across. The timing point for playing down the line should also be slightly earlier as its a shorter line and the ball arrives slightly quicker.
As you mentioned the finish position is very important wherever you are playing, to get the bat pointing forward and towards where you want the ball to go. As for some good drills, I think the est one is getting him to play 2 forehand drives across court and then 2 down the line, this is great for getting used to the adjustments needed for the different shots. Also helps get the correct timing point too!
