To best understand why the Eon Trio are the way they are, you'll have to go back to the source. Evan and Bonnie La'Vee are exceedingly rich, owning La'Vee Resorts, a chain of hotels in most of the surrounding islands and with Eevee Island itself. They had high expectations for their children, to the point of being controlling, having decided exactly what evolution their children would be long before they were even born. That said, they also have no business raising children, as they are pretty terrible at it. Evan and Bonnie spoiled their first three daughters, and Rosie, Shockette, and Bubbles would get their mannerisms from their vain parents. Eventually, Evan and Bonnie grew tired of the way these children behaved, despite lacking the self awareness that the apple doesn't fall far from the tree, and threw the girls out of the house, considering them all disappointments. Before leaving, Rosie took Joy, their new favorite daughter, with her to protect Joy from following the same pattern of influence and eventual self destruction.
Rosie herself is very much a product of her mother, but in spite of her, has vowed to be a positive influence instead of a negative one. She does her best, but every now and then she falls into the same patterns that her mother does. She is very vain and self absorbed, but in a way that's not malicious. Instead, it's more that she's oblivious to others rather than thinking others are beneath her. At the beginning of the series, she would talk about herself and the things that are going on with her more than listen to others, finding ways to bring a conversation back to her. This is done by habit, as a simple nudge to let Rosie know that she's focusing on herself would have her apologize and reshift focus back to the matter at hand. She is easily the most outgoing and talkative of the Eon Trio, which is saying a lot considering how much they all are. She is also just as flirty as Shockette and Bubbles, which tends to get a lot of guys red in the face pretty quickly. She's very spontaneous, loves shopping, and places a high value on fashion, to the point of her taking it seriously and hoping to get into couture. She is almost always seen wearing gold earrings. Rosie has an interest in travel and sightseeing for the sake of absorbing culture and expanding her own horizons, and this is something she really hopes to pass down to her sisters, especially Joy. Despite having had some repressed resentment against Joy because of how much better she was treated, she would try to rise above it in order to give Joy experiences that would make her appreciate the world, and make her a better person than even Rosie herself. Joy would always look forward to the outing shared between the two of them, hoping that they wouldn't end up in a name calling fight.
Rosie cares deeply for her sisters, and feels it's mostly up to her to protect them and to undo the damage set in by their parents. She seems to be the least broken of the Eon Trio, with Shockette having feelings of hopelessness and Bubbles diminishing her self worth. Though she wasn't above them, she hates to see her sisters fight, and she was always appalled and possibly the most hurt by the hateful things Joy would say about them to their face, making Rosie herself feel like she has failed in her role to care for her sisters and to make life better for them.
She is currently in a relationship with Meowth, much to his elation, and it has helped the both of them become better people. Rosie has learned to be more receptive to, and to look for non-verbal signs of the needs and wants of other people. Meowth has also learned to understand women better and has given him a reason to get his act together. By the series end, this relationship has helped make Rosie less self absorbed and more open. This, along with having broken the cycle of bitterness with her sister Joy has made Rosie a much better person by the end of the series. She's a lot more confident and is ready to take the world on while being on the lookout to lend a helping hand. And if any of her sisters need her for ANY reason, be it a place to stay or for potential opportunities, Rosie has let each of them know that she'll always be there for them.