I think Annie's father knew all along that Annie would become a Titan. I say that because Annie's father was the one that taught her the kicking move and if you pay close attention, every time she does that kicking move her left hand would instinctively cover the back of her neck. In other words, Annie's father taught her that move whilst having in mind that there would be a need to cover her neck.
My theory is that Annie's father had some say, albeit reluctantly, in Annie becoming an infiltrator and now regrets that decision but it's too late to take that back. I say he is reluctant because if I recall correctly he basically said you should/must/whatever hate the world and that your father is the only one on your side. Does the "world" include everyone inside the wall PLUS the side that Annie is supposedly on? If that is the case, then even though Annie and her father is on "that" side, he distrusts them for whatever unexplained reasons. And despite hating his side, he knowingly trained his daughter to fight for them which makes me think that his father felt some pressure to comply with them.
