I like a few things there, and there are some other things I’d keep the way they are.

“But Leia feared the hatred that turned our father” - I don’t think it was hatred that turned Anakin, hatred only came about once he had already turned. We can still use this wording, but it would have to use “anger” instead of “hatred”. Think back to Yoda in TPM - “Fear is the path to the dark side. Fear leads to anger. Anger leads to hate. Hate leads to suffering.”

I’m always going to disagree with wording Padme’s part as an afterthought, it needs to follow similar syntax to the mention of their father. You have to ask yourself: “Does this sentence make sense still if we exclude this reference?” If it does, then it’s fan-service, and not actually integral to the plot.

“Throughout her life” is necessary instead of what you have so that we can include Alderaan’s destruction and not just what she looses after declining the Jedi path. I prefer “still” over “always” only because it’s meant to emphasize that she was able to hold onto her ideals despite her circumstances.

I’d nix the “Rey” part, but the rest of that sentence is worded well. So, putting everything together:

“She was quick to learn in our training. But Leia feared the anger that turned our father, deciding to lead the galaxy with our mother’s compassion. Throughout her life, Leia lost everything, and everyone, but she still chose love. A thousand generations live in you now. Let Leia’s legacy be your guide through the darkness.”