I had similar issue last year before my Osaka/Kyoto/Tokyo trip. Now we're going again for 2nd trip, haha.
I'm not so sure how your approach is like, and each person has different personality, but for me, I also needed to convince her, this is what I mentioned:
1. Fukushima is from where we were going, and it's not airborne, but in the sea around the area.
2. Most of the seafood we eat isn't from the area, or is actually imported as well.
3. Radiation readings in the areas that you would visit is actually not very different from other places around the world as well (naturally occurring radiation).
4. We are only going for a while, as opposed to Japanese who live there everyday, they would also want to conceive and have healthy babies too, similarly you're not being reckless or irresponsible, you wouldn't want your future baby to have any health issues too right?

I had multiple discussions on this, and also went online together with her to research on the topic. End of the day, it's between the both of you, family and all that. On the other hand, if she feels really strongly about it, I would prefer to prioritize the feelings/emotions of loved ones. Its up to you to see whether a trip to Japan is worth the arguments etc. You wouldn't want to be seen as being selfish or calculative too. Good luck bro.