Once again, there’s probably a simple solution that I’m missing, but not finding it. In writing for SATB choir, there are times when one voice group should sing different notes. Ideally, the stems of each should go in different directions. It seems that despite the various “force stem” commands, they always go in the same direction together (see attachment). How can I order them to go in separate directions?
You’re looking for Voices: see https://steinberg.help/dorico/v1/en/dorico/topics/write_mode/write_mode_voices_inputting_t.html for a description.
What you’re missing is voices. In write mode with the caret active, hit “Shift-V” and you will start entering in a new voice. The little note indicator near the caret will help indicate which voice you’re in and which direction the stems will go. I also highly recommend going to the View menu though and under Note Colors selecting “Voice colors”. Makes it easy to see which voice notes belong to.
If you are new to voices, just remember that once you have created a voice, just use V (and not SHIFT+V) to toggle between established voices. Using SHIFT+V again will create an additional voice, which you may or may not want.
Is it possible to completely remove a voice once created?
Silly question, but before I knew about toggling voices with V I created new voices every time I needed another one. I realized that first when I found about 10-12 voices on one instrument in Play mode. So for that reason I’d like to clean up the mess a bit, is that possible? 
Unfortunately not at the moment, no, though I hope we’ll be able to do this in due course.