Oh no doubt. Hell it was a shock to me, haha.
I would like to add that there is a bit about competing with an alien for someone's affections too.
Competition between siblings for their parents' affection sometimes happens especially in the initial days.
And as Alex says in the pilot or LiveWire, after Kara came, it would appear that her role was protecting the newcomer and make her feel at home (as most elder siblings are expected to do even if the newcomer is not an alien) while the Danvers tried to make her feel at home. To top that expectation the newcomer had all these powers. It would have been natural for her to think that she would never reach Kara's level in her parent's eyes.
And then, you have the fact that despite the resentment, Alex ended up loving Kara because Kara is Kara! So, you have guilt on top of resentment because hey you are resenting someone who is such a great person.
And then, Jeremiah dies, and Eliza depends on her more, and she doesn't get to hear any word of support or encouragement. It is all on her.
I think she would have in time, accepted the fact that that is what she is supposed to do; and that Kara would always be first in her mother's eyes. Accepted it because she ends up loving Kara herself. And she decides that she would do her best to protect Kara.
But then, Clark comes and suddenly, it is all about Clark for Kara. And during that loft conversation, Kara even says that Clark makes her feel less alone
and she feels like someone finally gets her. (which suggests sporadic connection with Clark at best).
It must have hurt Alex really badly. And when Kara said that she would move away to be with Clarke it would have been like telling Alex, no matter what she does, she will never be enough for Kara. That Clark will be Kara's family. Add to that what Kara said in Falling and it is not surprising she laid out a case for why she could be enough; why she could be as good as Clark for Kara. Because she is thinking she is losing someone she loves, again, to someone she cannot compete with. Because she thinks that love is something you have to deserve by doing certain things (intentionally or unintentionally, her parents taught her that).
Laying the numerous reasons why she is good is not what she should have done.
Because Kara deciding to go was not about that at all; I think it was about her running away from new boss, Cat going on leave etc..
And also because, while Alex is saying in thoroughly complicated way that "I am good enough to be loved by you." What Kara is hearing is "You have been such a burden on me".
What Alex should have done is tell her I love you and let us figure things out or call her out on that running away thing, but I think Kara saying she is moving away to Metropolis as if Alex didn't matter at all was, as you guys said, a shock.
Just wanted to add this bit of defense to Alex's behavior out here. Don't want everyone to thinks she was just jealous.

As for her thinking Clark abandoned Kara, I agree with Kelly. From her POV, it must have seemed so to Alex. So, she used that in her scorecard.