Is the atomized water spray that splatters onto clothing from the body of a child who wets the bed impure, thus necessitating changing the clothes?

If the water is not altered by the impurity (in color, taste, or smell), then it is pure. The washing water (ghusala) that is altered by impurity is impure, while that which is not altered is pure. If you doubt whether it has been altered by impurity, the original state is that it has not been altered, and therefore it is judged to be pure.