You can retain the sweetness. Absolutely every child, especially female, tries this. My sweet oldest daughter is now seven, and since age three she has attempted from time to time to mimic the snotty things she sees out and about-and some of it just comes naturally with no example to follow. Girls just DO IT. She was never permitted to do it though, it was nipped every time. When she was younger, it was brief warning and physical consequence if it continued, now that she's older, she can understand explanations about empathy with a threat of disciplinary action (but it rarely comes to that because we have always been consistent, and she does have a good spirit and wants to be nice). Many kids these days get away with it though and it increases greatly through teens.
Your tough love approach is great to an extent with a few check points: Keep anger out of your reaction when enforcing discipline. It's human to give a disappointed verbal reaction to her, or even angry, when she is verbally attacking you and showing a hateful attitude. But you have to remain calm to be effective in these moments. If you are not in a position to enforce, and she snaps at you rudely somewhere like the car, sure, yell back if you must (but it's just as effective to speak if you have discipline on deck) with a, "That is a really mean way to speak to me. I do not speak that way to you and if you do it again, there will be a consequence. That is very bad behavior and not nice at all." Make sure you mean it. If she does it again, make sure you enforce later, she's old enough to make the connection after the fact.
But if you ARE in a position to enforce, really make sure to be calm. I have said things to my daughter in a calm loving voice that have really stung her and nothing else was necessary. Now the most common comment I get is "She is so sweet." If I get eye level and lovingly say, "Sweetie, I understand you're frustrated and some girls act like that, but it's not nice and it's not allowed. Do I speak that way to you? Do I speak that way to anyone? Do you want to hurt people's feelings? (by this point she's practically in tears). Then DO NOT use that tone/mannerism/make that face again or I will have to _____(terrible consequence) because I love you, I know you are a nice person and I cannot let you act that way."
Again, this is hardly necessary anymore because she has never gotten away with little things unscathed past first warning so it never escalated and she knows better.
Just be diligent. She's older now, so rely mainly on respecting the fact that you know she understands, and you respect that she is mature and a good person. Don't revert to snapping back very often (you're human, but just understand the best scenario) or you're engaging in similar behavior.
Good luck, hang in there, be unwavering. All the sweet girls in my extended family were effectively disciplined for this and grew into awesome teens and ladies.