A lot of time passed between when Kirk and Carol met and when we saw her in TWOK. It's entirely possible she did have an English accent when they met and that it changed over the subsequent 20 years to a more American-sounding accent. People's accents change all the time.
Oh come on. Better not explain it at all than explain it like that.
It's a totally normal thing that happens to lots of people, especially if they live in different places.