There are two reasons the presence of Winona Kirk (James T. Kirk's mother) on the USS Kelvin in 2233 might not make sense:
(1) Family members of officers and enlisted crew generally weren't housed on Starfleet vessels on deep space missions at that time in history.
(2) In the Prime timeline, Kirk was born in Iowa on March 22, 2233. (See here.) Therefore, his mother was not aboard the Kelvin at the time of his birth in the Prime timeline. The timeline in Star Trek (2009) is supposed to be identical to the Prime timeline up to the moment that Nero's ship appears in front of the Kelvin. Therefore, the arrival of the Narada is, at first glance, insufficient to explain the discrepancy in Winona Kirk's whereabouts in 2233, and the corresponding discrepancy in James T. Kirk's place of birth.
According to Memory Alpha (see here), screenwriters Orci and Kurtzman insist that Winona is a Starfleet officer, although there is no evidence of this in the Prime timeline (and again, her biography should be identical up to the point of Nero's incursion).
Giving them the benefit of the doubt, this still only resolves discrepancy (1) from above.
For (2), the only thing I can think of is that perhaps she may have been awaiting a shore leave that would have allowed her to give birth at home on Earth, but Nero's incursion could have caused labor to be induced prematurely.
Therefore, the question becomes:
Was James T. Kirk born prematurely in the new timeline?
There is no indication of this in the dialogue exchanged by Winona, George, and the Kelvin medical officers during the battle with the Narada and the evacuation of the Kelvin, and she is already in a medical gown, suggesting she may have been in labor and prepped for delivery prior to the attack. Also, even in the event of early or induced labor, the time from when labor starts to when birth occurs is generally not just a few minutes (!). But premature birth is the only thing I can think of.
It might help to know the date of Kirk's birth in the new timeline. How far off is it from March 22, 2233?