Locked doors and other fabricated barriers (e.g., Elsa's gloves; the mountains) -- indeed, Frozen employs a good deal of symbolism drive home its story and characters.
I'm in agreement with what you've said, that the final product illustrates Anna as something more than what her surface attributes may imply. In comparing Luna and Anna, I quite agree that the former lost sight of the things truly closest to her heart, whereas Anna was prone to misreading the signs (e.g., the "romance" with Hans) because, as you said, she's immature and isolated. I furthermore had the sense -- and this is relying solely on the show rather than the supplementary materials -- that Luna's isolation was in large part self-imposed, and in that way she and Elsa were more alike. The difference between the two of them is that Luna expressed her frustration in the form of tyranny and jealousy, or "if they don't love me, I'll make them love me" -- a response which is actually more reminiscent of Hans. Elsa, on the other hand, simply wanted to be left alone; it was Anna who helped her recognize the joy of having friends and loved ones.
As it stands, though, it's hard for me to draw a straight line between the two sets of sisterly relationships.
I wholeheartedly disagree. The first act of the film was almost entirely dedicated to establishing their shared history. The whole point of "Do You Want To Build a Snowman?" was that both of them were living in different forms of isolation; yet they ultimately wanted to be together. Consider the fact that the first thing Elsa creates when she's in the mountains is Olaf, a snowman that she and Anna built as children (their final happy memory together): it's the tacit "yes" she always wanted to say to Anna but never felt at ease enough to pursue.
But, for want of a lame pun, we should bear in mind that sometimes people are frozen in time. Anna and Elsa necessarily share limited mutual development because that's how they've lived most of their lives: Anna pursues Elsa's company, but Elsa shuts her out. They're stuck in a loop, albeit one which escalates as Elsa's powers grow stronger. Frozen explores the lengths one (i.e., Anna) will go to rekindle what was lost; in other words, it's very much a tale of love frustrated (in more ways than one).
Contrast this to MLP: the emphasis on Celestia and Luna's past as displayed in the show was about the rift that grew between them. We're not treated to much background on the matter in the series opener prologue other than that Luna became increasingly jealous of Celestia; she was, in some literal sense, in her older sister's shadow. The resolution is quickly wrapped up at the end of "Friendship is Magic", largely because time was at a premium and the narrative's focus resided with Twilight and her friends.
I think the real attractiveness of Celestia and Luna's dynamic is what is left unsaid: what drove Luna to basically unleash the apocalypse on her own world? Did Celestia in fact do her best to assuage her sister's fears, or did she brush them off in the midst of other concerns (i.e., governing Equestria)? I'm hesitant to start drawing from the comics because they aren't acknowledged within the show's central canon. (I know there have been comments to the effect of describing the comics as having some sort canonical basis, although Andy Price admitted it's up to the reader to decide. If left to decide for myself, I would consider the comics as extracanonical, or non-canon, as a main element of canonical status is official consensus on the material's authority.) As far as the show is concerned, the mystery of Celestia and Luna's falling out is by and large preserved at present. That's fine by me, to be honest.