Congrats on the meeting with the principal, it sounds promising
As for S13 and D10, probably better for you to not offer to be in the middle of their R with their dad. Authentic interaction with him will be better for them. Instead, you are teaching them how to manage various peoples feelings (including your own) rather than being true to themselves and direct.
PROBABLY ENOUGH SAID. Avoid 4x8 by skipping the rest of this post.
As for S13, after he saw your pain and struggle with seeing XH's significant other (she is not the other woman, there are not three people in a romantic R), S13 was probably more honest than you wish he was when he asked her not to attend to protect you.
I'll tell you this: I have protected my mother's feelings all my life. I was taught to do this to keep her from having a breakdown of some sort. I knew it was my job to help keep her stable. As a result, I was alone through many of the worst things that have happened to me in my life. There is no way that I would have shared my troubles with my mother when I was growing up, and there were terrible things that happened to me. S13 saw your pain at seeing X's GF. It doesn't matter that it was a few seconds. If you want your kids to feel safe enough with you to come to you with their problems, then you need to be strong enough to be OK with how the world is today.