Well, I'm certain there's no denying that the way you've viewed Touko as a character would be different from someone like me, a person who's been a fan of her all along, but I'll do my best to help you try to see her from a different light.
First of all, I'm not quite sure if what you're considering rushed is the pace of Yumi and Touko's relationship or the fact that the story has been somewhat shoving you personally into the affairs of a character you don't all that care for or pay much attention to, and you're begrudgingly having to put up with it. To be honest, I'd say Touko had been warming up to Yumi since the end of the second season (if not sooner) during the Parasol wo Sashite episode. That was roughly early summer -- it's getting close to Christmas now. And of course, thinking about it in real time, that was nearly 5 years ago for some of us who watched Haru during its airing. It can't possibly feel rushed from that perspective.
However I'd agree with you that at this point Yumi's still indifferent toward whom she chooses as a soeur. Just looking at this episode for example, though she eventually thought it a good idea, Yumi was not the one who first thought to invite Touko to the Christmas party. It was probably not even something she was planning to do. But although she may be indifferent, that doesn't mean she isn't still a nice person. If this were the tribulations of almost any other character in the cast, she would probably stick her nose in, and yes, even dissect them a little (I wouldn't really call what Yumi is doing "fantasizing"....) in an attempt to help them out. The issue simply is that Touko is the character in question, who is a first year. And as such makes her a potential soeur candidate for Yumi. Of course, Yumi probably wouldn't even had begun thinking of such a thing had Sachiko not made that proposition at the end of the school festival.
But Touko as well hasn't really taken leaps and bounds in terms of changing how she treats Yumi (at least externally). She was mean to her in the second season, and she's mean to her now. But even she has the decency to thank a person for their help, which I suppose can be considered the warmest thing she did to Yumi this episode. Factor in the basis that underneath her vitriol Touko probably likes Yumi very much, and her actions make much more sense. And I think it is a bit obvious that Touko likes Yumi, at least a little bit, from what we've seen of their interactions so far in this season and the last.
And as for their infamous first encounter, I completely agree with what Anh_Minh already said. Something like that probably doesn't bother Yumi that much anymore, since she's had time to not only shed quite a bit of insecurities, but also find out what kind of person Touko was herself.
And of course Touko's also to blame. Frankly, I think it may have been her idea to begin with. I've always liked to think that Touko had in fact heard of this "Yumi" before entering highschool -- a lot of Sachiko's family members do know about Yumi after all. Perhaps she in fact thought Yumi as a rival before Yumi even knew of her existence. Imagine the irony in Touko ultimately ending up liking her instead.
Ahh, but now I'm just letting my imagination get ridiculously out of hand. ...Forget that last part......
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