It's technically ok, but it isn't the clearest translation :) In English conversation, emphasising again at the start of the sentence often means you are reiterating a point for clarity or repeating yourself because someone isn't listening. I don't think in keeping with the sentence we're translating, here.
The differences are... cultural. And personal. Generally, the three main meals are: śniadanie, obiad, kolacja. For most of the English speakers it's either: "breakfast, lunch, dinner" or "breakfast, dinner, supper".
"Drugie śniadanie" is "second breakfast". It seems to me that lunch is 'too much' for it, plus I'd rather eat it before noon, but again, it may be a personal case.