I will say, I remember being in your shoes when my first was in kindergarten, and I wanted every interaction to be positive between him, his peers, and authority figures. The truth is, though, looking back, you learn a lot more from having to navigate through prickly relationships than you learn being treated very sweetly all the time.
I don't know what happened on the playground, but I suspect as you do that the older teacher spoke sharply toward her, sharper than needed for maybe something your daughter didn't even realize was a problem.
At this point - I'd stop trying to look back, and begin to look forward. It may well be that your daughter doesn't remember what was said - just how it was said, or how she felt about how it was said. I don't think continuing to question her about this incident is in her best interest.
What can you do to make outdoor recess more fun? Are the kids allowed to bring toys for recess? Maybe a couple little matchbox cars, a couple little fabric dolls, something, to play with her friends during recess?
It's okay for you to say "some people don't treat other people very nicely, she must not be very happy", or "sometimes you just meet quirky people and they don't act nice like the other teachers". But I wouldn't let her continue to dwell on it.
Next year, she'll also encounter teachers who don't treat her 100% fairly and kindly. And the next, and the next.
It'll be ok.
I agree with Rockrose. There is a very good chance that it was not what was said, but how it was said. In which case, your daughter probably would not remember the words. And since it is now going on two weeks - there is a good chance that she could not remember the words any way.
Perhaps the aide in her room could walk out with her and keep an eye on her for a day or two? Or the teacher could get a friend of hers to ask her to come and play?
But frankly, if your daughter continues to not want to go outside and you really want to deal with this. You need to nicely talk with the old grey haired lady (with the principal's permission - don't make this a surprise). Just say that she somehow apparently scared her a bit, and you wonder if she could go out of her way to talk with her and make her feel better.
As Rockrose said, its time to look forward.
As a Pre-k teacher, many flag go up when I read your story. If your daughter does not want to be outside with the other teacher, that tells me that this teacher has made her environment feel unsafe more then just one time. It is time to go back and talk to the principles. If you have made a complaint and he told you that he will take care of it, you have a right to see the report and what action were done. Let them know that your daughter does not feel safe and you want to know what was found out.
I agree with Teacher321.
Some children are so impressionable at such a young age, the tiniest issue can have a huge impact.
I would be insisting on a meeting with the principle and the 'grey haired lady' to get to the bottom of the situation once and for all.
During the meeting, I'd ensure that my daughter was assured of her right to speak about what's worrying her and that her feelings were just as important as anyone else's.
If the grey haired lady didn't mean any malice or disrespect than she'll be mortified to think she's caused such unrest.
If the principle appeared to know who the lady in question was, I'd be asking why and enquiring as to what investigation, if any, had taken place.
It's a huge thing for a 5 year old to suddenly feel that their safe haven isn't safe anymore. It's bigger in their mind than it is in reality and can so often be remedied with reassurance and patience. Go back to the school and insist that this time a thorough and remedial action plan is put in place with robust monitoring. Good luck