Is it permissible to suffice with rinsing a child with water without ensuring cleanliness by wiping after defecation, given that traces sometimes remain on clothes, and is it permissible to disregard the slight trace remaining on the tissue after rinsing and wiping?

Washing the anus with water is sufficient to remove impurity. It is more cautious to do this with the hand. If the bidet completely removes the trace, it is sufficient. The sign of purification with water is the return of the area's roughness. As for purification with tissue, a trace remains that only water can remove, but this is excused. The sign of its sufficiency is that the last wipe comes out clean. Purification with water is indicated by the return of the area's roughness, and one's strong presumption of purity is sufficient to avoid hardship. It is sunnah to perform istinja' with stones then water, and it is permissible to suffice with either of them, but water is better because it is more thorough in purification. Therefore, using the bidet is sufficient if the area's purity is achieved, especially for a young girl who is not yet obligated to pray.