[SAump]

I am still trying to understand what actually happened. You did not state that R1 passed R2 on the based path. So literally, the runners never passed each other. However from your description, I believe you. Maybe they did pass each other somewhere; perhaps as soon as R1 touched the plate, or perhaps R1 passed as R2 was on his way back to the plate. Then you provide additional information that should, by rule, not change the outcome. Surprisingly, from what I could determine, I think you were technically correct in both cases. The third out was made at the plate, but does the run count in one play and not the other? Nope! See Rule 7.12 below.

What if R1 realizes what is happening before he touches the plate, or after he retouches home plate and returns to 3B and while the play between R2 and the defense at home plate comes to a conclusion? I am only trying to describe all the possible scenarios on this play. Technically, I'm inclined to end it before all action comes to a complete stop and weird things (like a fight) break out. With less than 2 outs, the ball is live and the possibility of at least one run exits.

Rule 7.12: Unless two are out, the status of a following runner is not affected by a preceding runner’s failure to touch or retouch a base. If upon appeal, the preceding runner is the third out, no runners following the preceding runner shall score. If such third out is the result of a force play, neither preceding nor following runners shall score.