Annie and the 2 others have not the same goals. But they probaly encountered each others before, maybe there are childhood friends but they haven't the same hometown. During the training session, Reiner was teasing them probably because he asked her help and refused.
Annie is fighting against humans only because of her father, she is the nicest of the 3 and the only one I consider as an anti-villain now. She has probably the most tragic past of the manga. Seriously, look at her face when she was about to be captured

, she is absolutely not a straight villain. Reiner and Bert destroy towns and kill a lot of people but Annie doesn't operate like that. She probably teamed up with them after the training session because they were annoying her. Still, she didn't attacked during the Trost battle, only during the expedition arc because she wants to kill as few persons as possible. She is probably ok with killing soldiers because they are warriors.
Can't agree more about Annie teaming up with R&B after the training session.
Reiner was picking on her during training, but after saving Connie on that mission to replenish gas, Reiner was
trying to say "glad you're safe" lol. So something must have happened in between.
Also interesting to note, when Annie is apologising (to supposedly her team?) Reiner 'forces' his viewpoint on Annie by saying "there is no point in saying sorry"(not really force, but you get what I mean.) There's a fundamental mindset between those two. Annie, being alone with her partner-in-crime, opens up herself by saying sorry to a dead person, and that speaks a lot about her (whether she was the culprit for the dead she was apologising to or not.)
At first I thought he just didn't want her to get hurt (and expose her Titan recovery gas thing) but now I think there's more to that (specifically Annie agreeing to Reiner on a certain thing, and Reiner is thanking her through "being glad she's safe.")
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But that still could be her putting her life in first, not the mission. I mean, sure, she risked her life, but what would be the alternative? Being captured by Scouting Legion. I don't think it's about witholding information or caring about the mission, she just doesn't want to be captured/interogated/tortured/experimented on. And wasn't crystallization her last resort?
I think that's a good point, picking up on the crystallisation, but I think it's a different situation. Let's leave the term 'last resort' aside for now.
In the forest, calling out to other Titans is a
gamble. She doesn't want to be captured, and there are other Titans in the vicinity, so she calls out to them, risking being eaten, but if the plan succeeds, she can escape. If it fails, she still wins because she is dead rather than captured (so no-one can torture her for info. But I'd say she looks like she's gambling, but her bets are on herself being able to escape alive because of her promise to her father.)
In her last battle, there is nobody else that could 'save' her. There is nothing else, no-one else she could rely on. She isn't able to kill herself (?) (Think about it, she's stuck in the Titan body, the moment she comes out she'll be restrained.) That is why she crystallises herself to prevent anyone from reaching her (getting info out of her.)
There is also a flashback seen in her last battle, I think she cares about her father enough to want to go back to him and tell him she's still alive, to keep the promise. Yes, this contradicts her gambling behaviour in the forest battle, but a gamble is a gamble and there is just as much chance to escape alive than being eaten. This is what she's saying about gambling to Armin later on.
But in her last battle, there is nothing to be gambled about. Her only choice is to stay alive anyway, and by crystallising, she can also prevent other people from reaching her (for the information she holds.) And staying alive is definitely part of her agenda,
given the choice. I think she wants to go back to her father/ keep her promise with her father after all.
To expand on my last point: If she still thinks she can go back to her father, then she believes there will be someone to save her. If she only wants to keep her promise with her father by simply keeping herself alive, then the moment she loses she knows she's at a dead end. She's quite a sympathetic character judging from how she apologises to corpses, so I wouldn't mind saying she's keeping herself alive to symbolise some sort of eternal hope in returning to her father.