Would Anka consider trying to meet with Laeynna more to get past the problems between them?
In situations of this nature, it isn't Anka who is unwilling here. It's definitely more a failing on Laeynna's side, which could objectively be valid on some level, if not a bit cowardly. (But something I tend to hammer in Laeynna's backstory is that she is extremely cowardly.)
Ankalei would like to have the ability to sit down with her sister and really talk about everything. That is understandably complicated. The older twin in her wants to comfort her counterpart and tell her that everything is fine and that it's okay. But the reality is that it isn't okay and everything is, in fact, not at all fine. The reality is that Ankalei really, really envies that Laeynna gets to live life in a way that Anka feels like she's personally entitled to, and can't and will never be able to. Because Laeynna took that option and that agency away from her. (Ironic when Laeynna has been obsessed with obtaining her own agency.) And Laeynna can't magically go back in time and undo things, so there isn't actually anything Laeynna can do to make up for this.
Ankalei accepts that what happened has happened. She also accepts that she can't change everything. She can say that she forgives Laeynna and she does understand why it happened and she understands that if Laeynna and she were brought up in a different kind of household, that likely never would have occurred. But it's a lot easier to say you forgive someone than it is to actually do it in action and Anka isn't sure how much of her is more likely to hold a grudge against her.
The other side of this, of course, is Laeynna. Anka can barely get Laeynna to stay in a room with her, and that's understandable. Laeynna experiences no shortage of shame over what happened, over not being a stronger, more resilient person, and essentially condemning Ankalei to this kind of 'life' that she never wanted and never asked for. Being in the same space is like slapping Laeynna repeatedly with "you did this you did this you did this look at what you did you filthy monster."
Ankalei understands that, too, and no matter how complicated her own feelings are regarding resentment, bitterness, anger, and envy towards her sister, she also isn't inclined to take any of that out on her. She doesn't want to punish Laeynna for this, but Laeynna likely expects punishment (or more likely, Laeynna will just punish herself infinitely because that is what she does).
Andaeros has tried to get them to spend more time together and sometimes it works, but it's pretty evident that Ankalei just feels uncomfortable through the whole thing and Laeynna really doesn't like it and clams right up, so it might be one of those situations where they may not ever have a relationship where they can hammer it out.
Of course, having that conversation may also provoke them to look at things and deem any kind of relationship a lost cause and they might just completely sever contact. Either way, it's definitely a two-sided situation and Ankalei can't be the only one willing to put any effort into it.