I think she's Pink's original Pearl that Pink fucked up when she got bored of her, like a doll she broke and didn't want to play with anymore. White Pearl was probably dedicated to her purpose, only ever wanting to do what Pink wanted, like the hologram Connie in Open Book, and eventually this drove Pink nuts.
Don't know what exactly she did, but she probably deeply regretted it. Regardless, the Pearl was broken in more ways than one by her Diamond's rejection. So White took her back and "fixed" her by brainwashing her into little more than a puppet, because why waste a Pearl? Besides, it's more useful than a Pearl with her own will.
Our Pearl acted the same way at first, to Pink's disappointment, but Pink wasn't going to repeat her mistakes. As White's original Pearl, our Pearl was probably made with more mental abilities than the average Pearl - a more sophisticated brain, and a higher capacity for imagination and creativity. This is what helped our Pearl break through her programming, inspire Pink, and develop a genuine relationship with her