Imperious
Without the sun of my life
Probably go a different way when she is married to Viserys for years, the most adamant Rhaenyra stan in Westeros.
And again the way you word "secure the rule of her son" feels misleading about the things she did. Makes her sound like a heartless monster killing cousins and uncles to ensure that her son rules. Which she didn't, she just fought proactively against incredibly harsh Inroborn raids that were ravaging the Westerlands.
She didn't kill any rivals, she didn't grasp for more power, she fought a defensive war for her homeland. And when they finally got the resources to get some revenge, she took the opportunity. Which is completely fair because I'm pretty sure most people raided by Ironborn wished that they could sail to the Iron Islands and start cutting them back too.
She also had a preteen child of her enemy gelded and made into a fool for her son. I think Rodrik Greyjoy was about 8 years old when she took him captive.
And again, in a setting like Westeros trying to crown a brother of us over ourselves isn't that out there. People in Jaime's day still defend Cole by stating that he was just trying to defend Andal customs by ensuring that a son inherits before a daughter. By the standards of her time she doesn't have to be all that grasping to think her son should inherit before us even before taking in the bias one could expect her to have as his mother. Point being that if she does end up thinking her son deserves the throne before us, then she is likely to fight very hard for it.
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