Yes, they would still be balanced because their masses would not change.
In both Earth and the Moon environments, the mass of the children remains constant. Balance on a seesaw is determined by the mass (or weight, which is the mass multiplied by the gravitational acceleration) and their positions from the pivot. While the weight of the children would change due to the different gravitational accelerations on the Moon compared to Earth, as long as the mass ratios (and distances from the pivot) remain the same, they would still find a balance. Thus, the correct answer in terms of mass is that they would remain balanced because their masses do not change.