I had to mull this over overnight. I will not criticize you for your decision. It is your's and your's alone. But, just to throw my 2c in, I don't think I would have been as accommodating.
1) I don't think I would have apologized, because I had nothing to apologize for. If anything, she should have apologized, though I doubt I would have suggested it (would have just elevated the confrontation). Regardless, she's a bully in her own right and I would resist giving in to her bullying.
2) I most certainly would not have accepted her as an assistant coach. She has already shown that even lacking a legitimate cause she will pro-actively create one as it suits her agenda. She will be second guessing your decisions to the end of the season.
"You have enemies? Good. That means you’ve stood up for something, sometime in your life." ~ Winston Churchill