If you say that the turning point can be neglected then there is no such thing as a different history for A and B, as both - according to your symmetry principle, or better special relativity - are moving relative to each other. With constant speed. Thus, A is older in B's frame, B is older in A's frame. Contradiction.

As relative motion does not distinguish A and B, what does? (I give you the answer: B turns around.)

@AdrenalinMob: Maybe you can make such a trivial calculation for us. I'd really like to see it.