Welcome to cruise-chat. I agree with Cruise Fanatic regarding reviews.
We're a family of three (including 16-year-old), and we originally booked a mini-suite on sister ship Norwegian Jade last year. While on the ship, I took a peek into one of them and was surprised at how large it was. "Mini-suite," however, is a misnomer, as it's essentially a larger version of a standard balcony cabin. Still, I would think it comfortable for a family of four. How old are your third/fourth passengers?
Bermuda is a fabulous destination... we've been there several times and are returning (on NCL) next summer.