I want to make sure I understand correctly. Both of you agreed on a separation, with the intent of working on yourselves as individuals. You also separated in order to work at being better parents? How so?
You were under the impression the A was over, before the separation. You and your W tried dating each other. Was that before you discovered the AP was still in the picture? Had there been an agreement to not date during the separation period?
Since the S was not to work on the M, was there some sort of deadline..........or was there an agreement that the two of you would resume the MR and live together again?
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!