The staff work hard and deserve to be tipped fairly, however with a large family it really can add up fast and I see nothing wrong with trying to save a little while still being fair to the staff.
One thing you might consider is reducing the room stewards tips on the 3rd and 4th person in the cabin (I'm assuming you're have one cabin with 4 and one with 2). Assuming you tidy up after yourself and the kids, the 2 extra people in the cabin really doesn't produce that much extra work for the steward. We always tip 1/2 for the kids and think that's fair.
Another thing you may find is that your kids prefer to skip the formal dining room in favor of one of the more casual alternatives. If that's the case, you may want to adjust their dining tips accordingly. Again, I would suggest 1/2 would be fair if they choose not to use the dining room since they are eating somewhere and using some service but not the full service that would be received in the dining room.
Tipping is really a personal decision and only you can decide what is fair based on the needs of your family. The staff work hard and deserve to be tipped fairly for the work that they do, but don't feel you have to tip the recommended amount if you are not using the services fully. It's a tip for a job well done, not charity.