I don't actually blame Hightower people for taking throne

In that time males were valued more for kings throne. Even Viserys was crowned despite being younger then his female cousin. Viserys was the firstborn son of King Jaehaerys' second son and his sister-wife.

Rhaenys (old blond woman who hangs around) is the only child of King Jaehaerys I Targaryen's late heir apparent and oldest son. Known as the "Queen Who Never Was", she was once a candidate to succeed her grandfather as ruler of the Seven Kingdoms but was passed over in favor of her younger cousin Viserys due to her gender.

In other words she was child of first son of late king. And Viserys was son of second son. So she was higher in line. But they chose man to be king. Because women were proclaimed Queens only if there were no males in near line.

It's the same with Rhaenyra. For a long time she was kings only child and everyone assumed she would be queen when he will die. But then he married and brought 2 boys. So of course boys would be chosen instead of a woman.

Rhaenyra has a lost cause. Not to mention her two sons have black hair. Meaning that glorious Targaryen blond looks would be no more when her son would take throne. While her brother Aegon had two perfect blonde children. People and nobles would always prefer Aegon as king then Rhaenyra.