Yet another idea. Goddamn bunnies.
Inspired somewhat by
this fic (note, I do not suggest reading more of that fic than is necessary to understand the general premise. YMMV). For those who don't want to risk it: Aang-Azula, enabled by convenient amnesia on Aang's part.
Now personally, I think that this is better reversed. Let's say that at the end of The Chase, with Iroh zapped and Azula escaping under cover of some fairly indiscriminate blasting by Toph, Aang, Katara and Zuko; Sokka happened to lob his boomerang at her and managed to whack her on the head on the return loop (possibly it runs in the family). Since she had no helmet or anything, this neatly knocks her out.
Not feeling it would be advisable to leave her with Zuko (who is acting rather aggressively as a result of Iroh's injury), the team carry her off, planning to leave her at the next town in a random act of mercy. However, when she wakes she has - in accordance with dramatic cliche - no idea who they are and only a vague notion of who she is. When asked why she (an obvious Fire Nation noblewoman) is in the company of such a disparate group, Sokka tells her she's Aang's girlfriend: partly to cover it and partly because he knows that it will wind Katara up.
Of course, one lie quickly piles on top of the other and Azula soon has the functional idea that she joined Team Avatar at Omashu and is in the early stages of a star-crossed romance with Aang. She's aware that she has a father who she is defying, and a brother intent on capturing Aang (none of the team have a good handle on Zuko's status at this time). Meanwhile Ty Lee and Mai are chasing after the group, trying to rescue Azula (somewhat sabotaged by the fact that neither is willing to actually interupt Azula when she's having alone time with Aang (Ty Lee because it's sweet, Mai because she's concerned sappiness might be catching)).
Note that although Azula is re-establishing a personality as a 'good' person, she's no less determined and only marginally less capable. Ba Sing Se would probably unfold drastically differently with her along:
soulgriever13 said:
Sokka: I crashed a poetry class.
Aang: Went to a zoo.
Azula: Took over the local shadow government and made them my puppets. *everyone stares* What?
Zuko would probably discover what Azula's been doing (Aang) while in Ba Sing Se and feel some reluctant obligation to intervene, although he's uncertain who he would be saving from whom. Iroh is of course, glad to give the happy couple his blessing.
Of course, since things would be going entirely too well, Azula should recover pertinent memories at some point after this and leave the group. By this point however, her defection has been recognised and she's a wanted fugitive from the Fire Nation. The defense of 'temporary insanity due to getting hit on the head with a boomerang' probably won't work and while she's very angry with Team Avatar, it's not as if they exploited her particularly...
Azula: Why didn't you rescue me earlier!
Mai: There was too much suction between your lips and the Avatar's.
Ty Lee: And then there was untangling your tongue from his tonsils. So was he a good kisser?
Azula: (thinks back)
Mai: Azula, it's been ten minutes, are you going to answer the question?
Azula: How hard would it be for you to unrescue me?
So, after careful deliberation she goes back to establish a new dynamic with the group. Azula, after all, is an excellent planner and she knows what she wants.
Azula: Um ... hi? Azula here. *waves awkwardly*
Aang: You came back! (beat) Why?
Azula: If I go home I'm a wanted traitor in the hands of the Fire Lord's officials. If I stay here I'm a wanted traitor in the company of the best chance there is of overthrowing the Fire Lord.
Aang: ...oh.
Azula: Also, I was your prisoner for months and didn't get ravished even once. It's outrageous and I demand that you make up for lost time, Aang!
soulgriever13 said:
Sokka: (points accusingly) I know what you're planning!
Azula: Do tell.
Sokka: It's almost too terrible for words. First, you lull us into a false sense of security. Then you do the nasty with the Avatar. It's so obvious! You want your super-babies of doom to conquer the world and make you queen!
Azula: ...well, not until just a moment ago I wasn't.
Azula: (making notes) Sokka is annoying and ineffectual, but good at making plans. Keep him around as an advisor when I'm Fire Lord. Katara is sweet, kind and gentle. Also makes eyes at Aang when she thinks I'm not looking. Kill her with Fire. Toph...
Katara: I can hear you, you know.
Azula: Just fantisizing idly. I'm sure you're an expert on that.