Making a (mostly) likeable Tsundere

So I have one character in my original project, Tasi Shapiro. She is a girl (with injury sensing powers) who lived most of her life in the bad part of town with neglectful parents. She and her sister go to live with some old family friends when her parents' neglect is found out.

She is kind of bitter and doesn't like the protagonists because of their lifestyle and father's wealth. She's a decent person otherwise. She's a good if not sometimes protective older sister. She eventually grows to respect the protagonist because of his actions (she is of the 'earn my turst mentality). She is also planned to eb a Tsundere who eventually falls into a Slap-Slap-Kiss sort of relationship with the rival who is wealthy but also comes froma dysfunctional family like her.

The one thing I know I'm not going to do is play her being violent against him for laughs because I hate that trope. In fact her hostility towards him is mostly showed through words and the few times she does physically strike him she's called out for it.

When she eventually does start to see him as a love interest after they both save each other, she starts trying to get him to change unhealthy habits of his while denying that she likes him for awhile. He in turn tries to prove himself to her (not knowing that he already has a bit.)

First question does this come across as sexist or any other troubling implications? Second is there anything else I should do or avoid doing?

One way I decide whether something is sexist is to turn the tables. If it's okay for a man to do it to a woman, then is it okay for a woman to do it to a man? If you try it both ways and get different answers, then yes, it's sexist. That doesn't necessarily mean it's wrong or that it won't work in your story. Violence, as you say, is probably a bad idea.

Things to avoid? Season the Tsundere attitude with something else. For me it gets old in a hurry.

Personally, for me, the key to making a tsundere likeable is to portray them as emotionally messed up, rather than acting as if this behavior is acceptable, reasonable behavior or provoked by the target of their tsundere-ness. That's why I liked the tsunderes (or yanderes, depending on who you ask) in FruitsBasket. They, like pretty much everyone else, had serious psychological problems underlying their behavior.

^I plan on showing her behavior as a sort of defense mechanism. Her Tsun side also isn't reserved for just boys. It's more towards people she doesn't like, like rich people or people she thninks are spoiled.

It'd be an interesting deconstruction if she was forced to overcome her behavior. That's what I would expect to happen if the same thing happened in a non-Japanese work where the trope isn't played intentionally for Fetish Fuel. Whether through behavioral (self?)-therapy ("Next time Joe does something stupid I will NO yell at him...Now repeat that phrase twenty times."), or investigating the source of those traits ("Now that I have seen my old neighborhood, I realized that I hated men because of the lecherous neighbors always picking on me when I was a schoolgirl."), but she'd probably have to change her ways a bit - not neccessarily changing her completely, but a honest realization that she is acting in a self-destructive way, and some conscious effort to change. At the end of the day, relationships are mutual compromise anyway, so she'd be accepted (even loved) for who she is, in exchange for her trying to adjust her behavior and keep the worst in her down.

Not directly related but I once created a Mecha Anime story where the main pilot is a girl and The Lancer is a male Military Brat Tsundere who frequently tells her that he's keeping his eyes on her and if she screws things too much, he will personally kick her out, because really, REALLY hates the very idea of having a female in military. However, he mostly keeps the thoughts to himself and while saying fuck you to idea of chivalry (it's the setting where female militant is quite rare), liking making The Heroine carry heavy stuff and all, but he never goes out his way to be rude and apologizes if one of his worse comments about her incompetence and such hurts her. When she manages a mission well, which doesn't happen that much in the earlier season, he compliments her, even if it's through gritting teeth.

Does this counts as Tsundere and if it does, is he likeable enough?