I just tried a few things on my desktop and got some puzzling results because the
Always enter full mode checkbox on PhD's Preferences | General tab was enabled.
At first, clicking on the PhotoDirector button in PD momentarily minimized PD but then it came back a second later with no sign of PhD at all. If I manually opened PhD and clicked on the button in PD, a message appeared that PhD needed to switch to "Light mode" and would need to be restarted, but it still didn't launch.
After deselecting that option in PhD, everything began working normally when calling it from PD. Even after re-enabling that checkbox, the message about restarting in "Light mode" would appear (after clicking on the button in PD) but now PhD appears, operates and returns to PD properly.
My suggestion is to check and then uncheck that PhD option and try calling it from PD after each change and see if that gets the roundtrip functionality back.