How can I manage site translations in code?
I had the same problem and had a look at the module Features Translation. However, there were some downsides to it. Don't know exactly what is was. From what I can remember is that when I import a feature, for example the menu link labels are imported in the built in interface. So it doesn't help to import the translations for Menu Items because the source labels are not available there but in the Built In interface. But maybe I am wrong, tried so many things I can really recall what I did.

But you can have a look at it, maybe it works for you.

Tell us when you have found a suitable solution. I am curious.