Think of it this way: if both boards are just nested groups inside the DC, then the thickness of the horizontal board will also be scaled vertically and the vertical board will “stick” to this thikness nicely.
If you only constrain the horizontal board’s thickness to a fixed 3/4", then nothing changes for the vertical board. As you noticed. You should fix the vertical board’s local Z inside the parent DC to a position at 3/4" above the parent’s local Z.