AmyH - If you check out last summer's SWS trip reports in the sticky, there are details about the GC restaurants.
The short answer to your question is "it depends." You will not need a reservation to eat at Bright Angel, though you may have to wait a little bit for a table. I think for El Tovar dinner you will want to make a reservation now. We had lunch there with no reservation and got right in. We were early, though, before noon. It did start to fill up. Several others in our group had made El Tovar reservation well before going. If you are up in the air about it, your guides will be happy to help as well. You can tell them on the first day of the trip that you are thinking about it and they can check for you then.
Finally, the guides also took a group into town to the pizza place that night, so you might prefer to do that, if you or your kids have bonded with the group.
You're going to have a great time!