When I think about ideas for what could work for a Rosalina game, I haven't thought as much about how her character should be presented. How should she be at the beginning? How will she grow throughout the story? How should she behave towards things depending on what happens or in certain points of the game? It's interesting seeing you all express such distinct opinions that it makes me curious about what exactly is ideal for Rosalina in the future. We all love Rosalina here, yet even a small group of people such as us have different tastes in things and different preferences. Honestly, I'm not exactly sure about the ideal direction Rosalina should go in. She debuted showing that she is an independent, caring, powerful, and motherly woman who watches over the cosmos and an entire race of Lumas. Despite how the development process was when creating Rosalina, Super Mario Galaxy is still a solid foundation for her character. So good that it leaves us wanting more, yet we didn't really get that in the sequel. And since she's an already established character who can't go through too many changes like Zelda for instance, who has completely different incarnations to become more malleable to the games' plots, it's understandable to see portrayals of Rosalina in spin-offs as flawed. It's not exactly a smooth character transition going into each installment, but it doesn't matter to Nintendo as it has nothing to do with any sort of timeline when making spin-offs, and character development is not exactly a priority for Nintendo when making those games either. While I'm not as bothered regarding how Rosalina's appearances are handled in some spin-off titles as some others may be, I do agree that they can do better with her.
tl;dr: If Rosalina were to get her own game (which she totally should), how would you like her portrayal to be handled?