A trailer for Dog Days 2 is made available (h/t John).

Becky (and Shinku's sister) travel to Biscotti; Princess confronts Becky. They do not show who wins, but since Shinku has to return, your guess is just as valid as mine. But we may safely say that Eclair loses.

UPDATE: Steven alerted me to the fact that Nanami did not, in fact, travel to Biscotti. I suppose this error is understandable since I still call those island people "English". If you want more spoilers, watch the trailer for yourself.