Although I have never cruised with kids, I believe that you can check your kids into the clubs prior to going on an excusion. However, it's likely that they will not be able to reach you if there is a problem. I don't think the pagers they issue reach much further than the ship.
Some excursions do include lunch. The descriptions usually list what is included (lunch, open bar, etc.).
I always get early dinner seating and have never had a problem getting back to the ship on time. In some ports (St. Thomas and Grand Cayman come to mind), the ship will depart before the early dinner time, so it is not an issue at all. In general, you're rarely more than a half-hour cab ride from the ship.