I think a good question to ask is how her family treats/cares about their own image and how much they may want her to live up to that image. I have a good friend who comes from a fairly wealthy family, we've been friends for years and I had no clue she was as rich as she was until she actually told me years into our friendship. Yes, at times she could be pretty thoughtless, and there would be hell to pay if you didn't let her win an argument...but at the same time, she's really sweet and has a good heart. She was funny and we could talk about anime for hours. She's a really awesome person, but if you talked to her for more than a few minutes you could kinda tell she came from money, yet she doesn't throw it in people's faces or even take pride in it. She is very used to always getting her own way, and that does come through when you interact with her, but at the same time she is big into fairness and hates to see people bullied, heck, she was the kid in school that would stand up to bullies herself and defend the kids that need to be defended. She may be rich and a tad spoiled, but she's still a plenty likable person, and a person who faces real issues, just like you and me.
I won't go into too much details, but her family, despite having money, is not a happy one...and I think that is something you should take into consideration and keep in mind: just because a family has money dose not mean that family still doesn't have issues....it just means money is not one of those issues. Every family can have issues, regardless of how wealthy they are., and the same applies for wealthy people. Just as privlege can be great, it can also be not so great. While we may not understand the weight of living up to the responsibility of a family name, there are other responsibilities we do feel the weight of and thus we can empathize with a wealthy character who struggles under the weight of their prestigious linage. While we may not personally experience the isolation that comes with everybody wanting to be friends with us just because of our social status, we can still understand isolation and have been isolated for different reasons ourselves, and we still understand how lousy it is to be surrounded by shallow people.
Wealthy people can be as sympathetic or unsympathetic as you make them....just because a person has money dose not mean their life is one without problems or concerns. Just because money isn't a concern your protagonist has to deal with does not mean there are other concerns she does have to deal with that can still resonate with a non-wealthy reader.
Make your protagonist seem real...and you can't go wrong. Wealthy people are still human, and can still have human struggles and emotions. Your job is to bring that humanity out...so go, get writing. Thats the best advice I can give.
Btw, I also write a lot of wealthy protagonists, most of whom are villain protagonists, but not always. The current story I'm working on follows the daughter of the richest person on earth in a future where the class divide is far more pronounced than it is even now, and I think she's plenty sympathetic not in spite, but because of her wealth and the issues it brings.
This girl, like myself, suffers from high functioning autism and ADHD, and as a result has issues with living up to what her family wants, and expects, her to be. Her life is obsessively micromanaged by others and she herself is kept largely out of the public, left to live an extremely opulent but sheltered and isolated lifestyle so she can't do any damage to the family image when she invincibly dose something "weird" in public. Her public appearances are thus totally controlled, rehearsed and scripted. There is also immense pressure on her to do well so she can be the proper heiress the family business empire needs, but she just cannot live up to that expectation in most cases and it weighs on both her and her family. She is very rich, and a person looking at this world as a whole would likely find the sheer stark difference between the absolute excess in which she lives and the horrific poverty that the masses suffer to be disgusting and morally wicked.Yer, since the focus is on her we get to learn about her as a human. We get to see that she is a passionate VR gamer and anime otaku who lives for the catharsis of her escapist, digital fantasy worlds. We get to see that she is a programming genius. We get to see that she is weird in all the best ways, and she makes us laugh. We see she is honest to a fault, sometimes brutally so. We see how she hates seeing others bullied, and will stand up to bullying when she sees it. We also see that she faces real personal mental health issues made worse by a family that's not too happy about the fact she has them. You get feel her isolation with her..and how both her immense privilege and the fact the world seems counter to how her mind operates leaves her unable to connect with others and have actual friendships.
Most of all, we see her overcome all her issues, and become the unlikely hero. We see her go from being an aloof rich girl ignorant to the world's suffering and absorbed in her digital fantasies to a reality-warping hero who puts her life on the line in a quantum videogame, fighting an evil catgirl to liberate God's brain from her control and set reality right for everybody.
By focusing on somebody like her, you find out that she's not a monster, even though she is very privileged. Do this with your girl..make her human, and notva stereotype, and you'll be fine, I think.
