The Rizzo and Kenickie thing was pure high school romance, complete with game playing, drama and politics. It was obvious she and Danny had a "thing" the year before or so. So, was Rizzo just getting payback? Also, she was AWOL at Thunder Road.
The answer for me lie within your first statement. Its a high school romance, nothing real serious.
I think the scene in the Frosty Palace where Danny says to Rizzo "Bite the weenie" and she replies "with relish" sums it up perfectly. That says to me she is keeping up her rep as a bad girl, yet in the end "There Are Worse Things I COuld Do" spell out her true feelings.
And because she just poured her heart out as Kenickie was headed out to Thunder Road (that's him in the background of the song) There would be no reason for Rizzo to be at big race.
I think from what I can tell from the film, it seems like she had a thing with Danny but it ended badly. I kind of get the impression it was due to him and he did something and that's why she's so bitter and skeptical initially when it comes to guys ie. When Sandy's talking about him and says he was special and Rizzo says there's no such thing. I feel like she was really into him and then got her heartbroken so now she's kind of sleeping around and she has her bad reputation and people talk about her a lot which clearly bothers her a lot more than she lets on (evidenced when she says to Sandy 'You think I don't know what people say about me' yeah, at that point it's about her pregnancy but I think it's a common occurrence for her) so she puts up a tough front to protect herself from getting hurt by anyone. Then her and Kenickie start flirting and seeing each other and I think they actually do grow quite close but she suddenly feels vulnerable again and therefore closes up and builds a wall up between them which starts their argument and eventually causes them to break up. They then both go to the dance with the two people they know will piss the other one off the most (I feel like Danny may have cheated on Rizzo with Cha Cha hence why Rizzo and the other girls have such a dislike towards her and why Danny gets awkward when he sees her there, and obviously Kenickie and Danny both hate the guy) because they're both high schoolers who don't really know how to handle situations properly so they act out against each other. Then Rizzo realises she might be pregnant and that just throws her off even more making her even more emotional and vulnerable and she doesn't know what to do so when Kenickie talks to her about she, again, shuts him down to try and stop him from getting too close because she's worried that she'll get hurt. When Sandy then speaks to her and asks if there's anything she can do Rizzo goes to shut her down again (she's obviously got some resentments towards Sandy because she managed to get Danny to love her and want to be with her in a way that he never wanted Rizzo and she felt threatened by her) but in this moment she allows herself to show some of her vulnerability to Sandy because she accepts that Sandy is just genuinely trying to be nice and she realises that Sandy herself hasn't actually done anything wrong. She says thank you to Sandy which shows some of her own personal growth and then we 'There Are Worse Things I Could Do' which shows all of her vulnerabilities and her feelings and why she acts the way she does and it becomes clearer to the audience and I think herself why she's been behaving the way she has been. She didn't go to Thunder Road because she still had to contemplate what she was going to do and at that point still thought she was pregnant so didn't feel like hanging around a guy that she really does like (I do believe that she really liked Kenickie) especially when he might not even be the father because she made a mistake and slept with some other guy. Eventually she realises she's not pregnant and then she's free of that burden/worry and feels ok and safe to open up to someone, in particular Kenickie, hence them getting back together at the end.
Sorry about this essay! Lol! As you can tell I've given this a lot of thought!
I got the impression Rizzo was the high school girl that all the guy wanted to date because she was willing to put out. Odds are both Danny and Kenickie hooked up with her for that reason. We see throughout the movie Rizzo does have a heart and is much more, but it takes till the end of the movie for Kenickie to figure that out.