The setup in my photo, with the pivot behind the rear wheel, is designed so that the trailing bike follows in the rear wheel track of the leading bike.
This is great for off-roading on narrow and winding forrest tracks but is not the best design for isolating the lead bike from the antics of a wobbly child.
Your experience with the high and forward pivot point makes sence. In theory the best pivot position for stability is high up and on a vertical axis that aligns with the lead bike's rear axle. (This is a 'first class' lever arrangement where the mechanical advantage of the trailer bike over the lead bike is small).
Lower pivot point bikes, like mine, only work if the lead bike's rider is much heavier than, and has enough inertia to subdue the wobbles of the trailing rider.