That was a strange ending. What was the point of busting in with the dragon then? Just to show she could? If she was basically starting a war there she could have ended it straight away.
Episode felt a bit all over the place.
The weird daughter reminds me of the uni girl April that Mark dates in Peep Show. Also was weird seeing the kid from Shameless running round as two people.
It could have been a decent idea, had it been not executed so poorly. But, to answer your question, there was a purpose to her decision.
If you pay close attention, Alicent gives Blackfyre, the sword of Aegon the Conqueror, to her son for his coronation. After that, the crown placed on his head by Ser Criston isn't the same crown Viserys was wearing during his reign. His was a golden crown with the sigils of all the Great Houses engraved on it as a symbol of peace and unity. Aegon II wears The Conqueror's (first) crown. The one with which he proclaimed himself King of the Seven Kingdoms. A warrior's crown, black with red rubies as a symbol of Targaryen purity. The greens are trying to get a message through: We are the pure Targaryen blood, and there'll be no peace with anyone who opposes us. Rhaenys recognizes the symbols and decides to spit in their faces.
By not killing them, she's doing Rhaenyra a favour. She also declares, rather spectacularly, where her allegiance lies. Without revealing anything, this isn't the first time Targaryens fight Targaryens. The first time it happened, vile atrocities were committed, unspeakable brutalities took place, terror ruled the land and the Targaryen dynasty came close to collapsing. The man responsible for the bloodshed was anathematized in Westeros, and became an example to avoid in his own House. Another important detail is that he also was a brother trying to take the throne from his nephews. With civil war at the door, the blacks don't want the first Targaryen blood to be on their hands.