Yes, for you the Greens were usurping the throne and it was a coup against her family and brother. I think she would agree with that.
Now for the “so what?”. Does she really see it that way? The proper heir, who was possibly involved in killing her son. That heirs now uncle/husband was married to her daughter who died struggling with birthing his spawn.
I think Rhaenys showed who she is in that throne room once Visarys came in by stepping forward and now taking Rhaenyras offer. She’s calculating, she plays both sides down the middle. And that’s what she was doing here. It was just highlighted with sloppy fanfare.
I don’t think she holds particular interest to any side, but Driftmarks side. And she’s going to let these two sides go at it and leave herself on the fence and ready to move on with the winner…..”for the better of the realm”…..and Driftmark/her kin.
Or maybe said a more simple way….would she torch Rhaenrya and Daemon if she had them in sight? So why should she torch the new king on stage who, along with brother and sister, are also kin?