It isn't cheating. It's fucked up, but it's not cheating. Nothing was inserted into anything, there was no kissing, blah blah. It's obviously sexual, though. Because if it isn't, wouldn't that mean it's fine to just grope asses and dicks and stuff as you please? It's dancing, yes, but it's also sexual; there isn't really a case for mutual exclusion there.
I guess the question here is what makes cheating cheating for you? For me, it's a question of intimacies; are you emotionally intimate with this person in a way that is romantic (lovey-dovey shit)? Are you physically intimate (not just sex, but cuddling, kissing, allowing spanking or other groping)? Shaking ass at a club to have fun is shaking ass at a club to have fun; you might not like the image, but that's her enjoying herself, and non-reliant on another person. Guys come up to dance with her, but she's attractive (presumably) and she's in a club, which is where you go to dance with and pick up people, and that's how folks dance with each other these days. To the folks judging her for how she dances, do y'all even go out to dance? I mean to a club, and not just like salsa dancing (which strikes me as a lot more sexual with the leg-wrapping-around-the-waist stuff and all).
Whether OP breaks up or not isn't for me to give input on, but her "feeling bad for how it made you feel" is a perfect non-apology. I used to use all the time when I didn't feel bad at all for my actions but felt bad that my partner was troubled over it. She's saying there's no problem with her reaction, but it sucks that it bothered you. My advice would be to have a talk about it, because it sounds like y'all have some different perspectives on the shit and if her way of fun and blowing off steam feels like cheating to you, it's worth knowing where her line is vs. where your line is.
Personally, I wouldn't dump a woman that I was dating if she did that, but I also would NEVER EVER want to hear about it unless there was some problem or something. I don't think it's cheating, and I would dance with women like that, so it'd be hypocritical of me; but I would make sure my S/O wouldn't hear about it, because sometimes, you just have to be prudent about the info you're sharing. It sounds nice to say that couples should share everything, but rare is it that you know a person with whom you can share everything and anything, especially when you get into the tangled mire of love and jealousy. Is she good to you? Does she help you when you're down and do you like spending time with her? Do you trust her most of the time (I wouldn't ask 100% trust of anyone, but like, 80 or so is a good point)? Can y'all resolve arguments in a reasonable fashion without lingering resentment? That's the shit that's important. If she likes to shake her ass at a club to have fun, is that a big enough deal for you to walk away from all the good?
If she's a keeper, she's a keeper. No one's perfect; the question is just what flaws (perceived or otherwise) can you live with, and which you can't.