Note that the expression in Sanhedrin there is שולט - dominates. Antoninus (and Rebbi) might well agree that the evil inclination exists in utero, just that a person doesn't begin to act on it until birth.
R. Shneur Zalman of Liadi makes a similar point in Tanya, ch. 13. Having previously explained that a benoni is a person who has two equally active inclinations, to good and to evil, but who always ends up doing the right thing (as contrasted with the tzaddik, who has completely sublimated or even transformed his evil inclination, and the rasha, who to a greater or lesser extent does evil), he writes (translation from here):
Therewith will be understood the commentary of our Sages that "'Intermediate' people are judged by both [the good and evil natures], for it is written, 'He stands at the right hand of the poor man, to save him from them that judge his soul.'" Note that they did not say "ruled" by both, G-d forbid, because where the evil nature gains any control and dominion over the "small city," even though but temporarily, one is at such times deemed "wicked."
The evil nature [in the benoni], however, is no more than, for example, a magistrate or judge who gives his opinion on a point of law, yet it is not necessarily a final decision to be implemented in deed, for there is another magistrate or judge who is contesting this opinion. It is, therefore, necessary to arbitrate between the two, and the final verdict rests with the arbitrator.
Similarly, the evil nature states its opinion in the left part of the heart, which thence ascends to the brain for contemplation. Immediately it is challenged by the second judge, the divine soul in the brain extending into the right part of the heart, the abode of the good nature. The final verdict comes from the arbitrator—the Holy One, blessed be He, who comes to the aid of the good nature, as our Sages said, "If the Almighty did not help him, he could not overcome his evil inclination."
So Eisav's evil inclination was asserting itself, as was Yaakov's good inclination, but it was no more than that - an assertion. Things could still have gone either way with each of them once they were born. More to the point: granted perhaps that Yaakov was given the power to be a tzaddik and Eisav was not, yet Eisav could have become the ultimate benoni - whose service of Hashem in the teeth of the challenge posed by the evil inclination, as R. Shneur Zalman goes on to explain (in ch. 27), gives Him tremendous pleasure.
(There is also this to consider: each one's "running and struggling to get out" might itself have indicated one of two things. At a shul, for example, it might mean that the baby is naturally drawn towards its holiness, but it equally well might mean the opposite - that he desperately wants to get out and torch the place! Same thing, lehavdil, at an idolatrous temple. So Eisav's eagerness to get out when Rivkah passed the latter kind of place need not have been evidence of wicked tendencies - on the contrary, it could have meant that he has a powerful natural inclination to fight against idolatry, like his grandfather Avraham.)
