We've done Flying Fish with the kids; I think they had Mickey Pasta and they were very accommodating. The service was beyond excellent and the food was great too. The menu is definately heavy on the fish, but delicious dessert, and I think I had a wonderful soup that may have been on a special.
This may be weird but I think your children may be too little for ESPN...unless your 4yo is a sports fanatic...it's a bar atmosphere, and I feel like the seats are oversized and low and the tables are oversized and high? I'm short so it may just be my take, but I think we were there with the kiddos and it wasn't that comfortable for them and they kept dropping stuff and sliding under the table. And I think, someone correct me if I'm wrong, that you can't get an ADR so you have to put your name in and the wait can be very long.
But the Boardwalk is a great idea for the first night! The kids will love it, you can get a drink while you walk around and watch the performers or play the games, or you can rent a surrey for a pretty physical ride around the Boardwalk with your kids in a basket in front. Very fun. You can skip dessert at the table if they're itchy and stop in the Boardwalk Bakery for something to go. It's a GREAT take, very entertaining for everyone.
Have fun!