Sorry for shitting out a rambling wall of text. It'd take more time than I have right now to edit it down, and make sure I actually hit all the points I wanted to.
To be honest, Yui's decision to float off at the end has been a hard point for me as well, but in a different sort of way. That is, I have difficulty reconciling the usual explanation -- that she is leaving Earth to simply float in space for all eternity and have her soul seared by the inferno of ultimate loneliness -- with pretty much everything. I suppose I find it more thematically/narratively sound, and much more psychologically comforting, if she's leaving to "continue the cycle", as opposed to simply let it end with her.
So, essentially, I am biased toward wanting to think that Yui has taken it upon herself to save humanity both in the short-term -- i.e., prevent Seele from turning everyone on Earth into a Hive Mind -- and in the long-term, that is, become something capable of creating another humanity long after our own inevitable extinction. [This also allows me to make my own sense of Fuyutsuki's line, "mankind has existed to create Eva": in the sense that an organism exists solely to propagate itself, and in keeping with "human family tradition", our humanity existed solely to create a being who will propagate another form of us, long after we're gone.]
Since Yui has had this two-pronged mission from early on, embarking on her cosmic journey directly after Third Impact is only logical, as she has effectively fulfilled her purpose on Earth and done what she set out to do. People have been given rein over their own fates once again, and there is no longer any need for gods, including herself.
From the short-term perspective with which most people view the universe, leaving her son and everyone else with Earth in such a state is direly cruel, and can certainly motivate unbridled hate. But I think one of the things that makes Yui interesting is that she really isn't a normal person. I don't been that in a pejorative sense; even before she became an Eva -- which would most likely affect one's sense of time and priority quite a bit -- she's probably never been able to look at the world in the way an ordinary person would.
She was born as one of the elite and privileged. She's been subject to privileged and doubtless highly troubling information from early on. On the most basic level, Yui seems to be extremely benevolent and compassionate; that is, she has identified certain things as precious and worth saving that most well-intentioned and wholesome people would. For example, the right of people to live as individuals and pursue happiness without worrying about a bunch of old farts telling them that they all suck and don't deserve that chance.
Yui's deep love for humanity might also extend to the desire to see it exist even after the death of Earth and our Sun.
So consider, this person with nothing but compassion and a desire to protect what's most important. And consider what she is up against. A global cabal, and a rapidly ticking clock. On a personal level, she faces a conflict between the desire to simply escape from the curse of Seele and indulge in a comforting fantasy of ultimate normalcy -- getting hitched and having kids -- and acting upon the moral imperative to do something, ANYthing, to prevent the ultimate tragedy. Yui has to choose between the desire for intimacy and deep personal connections in her life -- expressing love for humanity one-on-one -- and in the desire to put her universal love for humanity into real, tangible action, because she has the burden of knowing that if she doesn't do the latter, nobody will be able to enjoy the former.
You've probably heard all this already. Where you really want answers, I can't exactly help, since Yui is and always will be inscrutable to some level. But, the best I can tell you is that she probably skewed a shitty situation as much as she could so that people would come to understand one another for the first time (HIP) and then be freed to march forward and pave the road for themselves. Of course, all of her ideals sound ridiculously naive and inane if you try to apply them realistically to a post-apocalyptic world, but as long as you're in sci-fi, humanity can recover from any setback. :3
And on that note, certain aspects of the ending and Yui's departure are a giant metaphor for mommy walking off and letting her boy deal with all the shit in the world without her magically showing up and making everything better. Or something.
NemZ wrote:How that hook up happened is one of the biggest blanks in the whole series. I think you're on the wrong track with the abusive angle though, as I actually have a really hard time seeing Gendo as anything other than completely whipped when it comes to Yui. I picture it as the sort of relationship where she knew she'd always win any argument and didn't really see the point in having them, instead simply not informing him of anything he might try to object to or only talking about when it's too late to change... lots of flabbergasted Gendo moments when he simply has no options and thus can only rage ineffectually for a while before succumbing to the inevitable.
So instead of taking a NemZ-ish stand against the character, why not gradually (re)appraise the various Yui analyses around these parts that don't necessarily jibe with you?
-- wouldn't have necessarily made things any better. And since Yui was a transcendental being at the time she left, she probably knew this. 
