I don't much care for the Gilded Age-ification of the Matthews family that happens in a lot of the popular fanon. The WASP old money high society thing, with debutante balls and sprawling estates and a herd of hired help. I'm just not interested in projecting such an intrinsically white experience of wealth onto Lottie, and I think there are other depictions that make more sense and are more nuanced to her identity.
Like, Malcolm Matthews absolutely screams workaholic yuppie. That man is not old money. He grew up in the middle class suburbs, classic postwar baby boomer style. He was probably the first in his family to go to college, and he became a finance bro that made a fortunate on Wall Street. Emilia is an immigrant or the child of immigrants, also the first in her family to get a college education, and she went into a high-paying profession like law.
So you've got Malcolm the nouveau riche yuppie, and Emilia the high-achieving immigrant. Two variations of upward mobility, the promise of the vaunted American Dream realized. They're moving up in the world with booming careers, and they cross paths at work, and there's a spark. They have a whirlwind romance, with marriage and a baby soon following, and Malcolm buys a penthouse as a testament to his professional and domestic achievement.
But it doesn't take long for the cracks to show. Malcolm and Emilia don't actually have that much in common, outside of being obsessed with their jobs and having a taste for the finer things. They especially clash when it comes to raising their child, and it only gets worse as Lottie's peculiarities become more apparent.
They send Lottie to a fancy private school in the city with other rich kids, and a lot of those kids do come from old money. They pick on her for not knowing the arbitrary rules of upper class social etiquette, for having the wrong pedigree and looking different from them, and most of all, because she's just weird and hasn't learned how to mask it yet. The bullying just exacerbates her issues and sense of isolation.
Malcolm and Emilia eventually divorce, and Lottie knows she's the biggest motivator and internalizes it as her fault. Emilia gets primary custody, and she moves Lottie to Wiskayok. She can't afford penthouse living in the city as a single mom, but between her well-paid job, the divorce settlement, and child support payments, she's able to buy a McMansion in the Jersey suburbs and hire a housekeeper, maintaining some of the lifestyle she's grown accustomed to.
It's a strange transition for Lottie, trying to adjust to a town in the suburbs and being the new kid at public school. In some ways, it's a fresh start. Her sudden appearance as the mysterious rich girl from the city gives her a certain mystique and glamour among the students, and she develops a good reputation and even makes some friends, primarily with her soccer teammates. But the feelings of loneliness remain.
Emilia still works in the city, where she commutes and occasionally stays for multiple nights. She's rarely home, leaving Lottie mostly to her own devices. Emilia's under the impression that Lottie enjoys having more independence without Malcolm breathing down her back, but she's really just projecting her own feelings. Lottie would rather spend time with her mom and thought the divorce was going to give them the opportunity to get closer.
Malcolm stays in his penthouse and has partial custody, but he doesn't exercise it as much as he could. He's usually distracted with work when Lottie visits, and he sometimes just cancels all together. In lieu of actual parenting, he spends money on fancy gifts: a birthday Rolex, a car for Christmas, chartering a private jet for Nationals.