Thank you to everyone for your excellent advice and support.
The other mother has just rang me!

She started off a bit high-handed and defensive, playing down the whole situation. I was having none of it, so putting on my best teacher voice, I told her that she was, under no circumstances, to speak directly to Olivia in that way again. I told her that her daughter had been (allegedly) upset by a child, but that my daughter had been left upset and intimidated by an adult - which I thought was totally unacceptable.
Anyway, to cut a long story short, she eventually cracked and admitted that what she had done was 'unforgivable' and that she had been worrying about it all weekend. She had looked at it from my perspective and seen that she had handled the whole situation very badly.
I was gracious (and told her that we should now just move on and forget it), as I had received an apology and an acknowledgement that what she had done was wrong. I told her that in future she should involve the class teacher or speak directly to me, and she agreed.
Anyway, all done and dusted now. Until the next time.