Is it obligatory to search for places where the child sat and purify them if stool came out onto his clothes, given that no trace of the impurity is seen, and do wet wipes remove the ruling of impurity?

As for obsessive thoughts (waswas), strive to repel them. If you doubt that your child sat in an impure place, you are not obligated to purify it.

If you are certain that impurity has transferred to a place, you are not obligated to purify it except when you intend to pray on it.

A wet wipe does not purify impurity; rather, water must be poured.

If you touch the impure spot after wiping it with a wet wipe: if both the spot and your hand are dry, the impurity does not transfer. Otherwise, there is a difference of opinion regarding it.