Why in the world would Einstein suggest....

https://www.google.com/?gws_rd=ssl#q=peter+hayes+relativity

Dr Peter Hayes is senior lecturer in politics at the University of Sunderland. In his latest paper ‘The Ideology of Relativity' Dr Hayes argues that Albert Einstein's theory of relativity - perhaps the most famous scientific theory in history - should be viewed as an ideology, not as a science. He argues that its impact on popular culture and science has been so influential precisely because as a scientific theory it doesn't actually make sense...

A famous flaw in Einstein's theory is the Clock Paradox. This states that if one clock travels in a spaceship, while the other stays on earth, when the clock in the spaceship returns it will show that less time has elapsed than the clock on earth. This prediction violates Einstein's own ‘principle of relativity', which states that if you are on the spaceship it should be the clock back on earth that slows down. This is a criticism that science has never been able to satisfactorily resolve....

[Hayes says]: "Precisely because Einstein's theory is inconsistent, its supporters have drawn on contradictory principles in a way that greatly expanded their apparent ability to explain the universe. Most crazes die out when it becomes obvious that they were overblown. The amazing thing about Einstein's theory of relativity is that it has kept going. It is built on contradictions, but these very contradictions means that almost anything ‘proves' that it is right. It is a bit like a theory where you say 1 + 1 = 2, but also that 1+ 1 = 3."

2. Theories of motion which do not impose this artificial and very dubious requirement on observers make all the same predictions, just as well, as does SR. "Relative simultaneity" is by no means required to explain relative motion. SR cannot be said to be superior on the basis any experimental findings or other empirical grounds. SR is not a "proven fact."

Clocks that are far from massive bodies (or at higher gravitational potentials) run faster, and clocks close to massive bodies (or at lower gravitational potentials) run slower. This is because gravitational time dilation is manifested in accelerated frames of reference or, by virtue of the equivalence principle, in the gravitational field of massive objects.[3]

Albert Einstein's theory of relativity

Does my proposed hypothetical address the question...

To claim that the clock paradox is violated when you ignore the theory of general relativity is not proof of anything other then you don't understand relativity

...but when B is accelerating the A's clocks run faster to such an extent that the overall elapsed time is measured as being shorter in B's frame

Since B's route involves acceleration, her frame cannot be considered an inertial reference frame and thus none of the reasoning applied above (such as time dilation) can be applied. To deal with the situation in B's frame we must enter into a much more complicated analysis involving accelerating frames of reference; this is the subject of General Relativity.

(2) what if B instead circumnavigates the Universe so he undergoes no second shift of frames