Our gray water tank is what fills up first. We don't take showers except at the campgrounds where they provide them. Not a big deal to go a week without a full shower. With your children I would stay at campgrounds with showers. Then the only thing going into the gray water tank is from the sinks which should be very little. We don't make dishes like spaghetti where we have water to dumo as we want to conserve both our fresh water supply and the space in the holding tank.
We also use the available toilets at campgrounds and minimize our use of the one in the camper. It makes for fewer stops at dump stations as we travel.