Welcome to the board.
We have kids of similar ages. Ours are 5, 8 and 12. We have been vacationing on the island for the past 12 years always with the kids and occasionally just my wife and i in the fall as well.

As far as dining goes I've come to the realization that it's best and most relaxing tojust play it out and let the island time and your families rhythm control where and when you eat. Sometimes it feels just right to take in the late evening breeze, let the kids swim till dusk and skip the reservations.

We like to put a wish list of restaurants together and take turns picking out between the family members and sometimes just swinging a door open to a new place and trying the fare.

My suggestions for your list are limited to
Linda's pancakes - unless you like to sit around for an extremely long time waiting for one pancake at a time with the hungry kids I would avoid this establishment. My personal opinion you can formulate your own.
Smokey Joes- we love for dinner. Avoid the long wait for the all you can eat ribs night.
Try dushi bagel behind la playa Linda for breakfast and/or a tasty and economical lunch.

Like my accountant says "Expect nothing and be pleasantly surprised!"
Enjoy your family vacation..you'll be back!