All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The ablution of a woman who washes a child or even touches his private parts is valid and not annulled as a result of this act according to the preponderant opinion of the Muslim scholars. In fact, the touching of the private parts that nullifies the ablution is the person's touching of his /her own private parts.
Moreover, the reason the scholars believe that touching the private parts nullifies ablution, is the touching that arouses the sexual desire, which does not exist in this situation; i.e., when a woman touches her child's private parts. Imposing ablution on a woman for this touching causes much hardship for her. Allah Says (what means): {…and has not laid upon you in religion any hardship…} [Quran 22:78]
Therefore, you are not asked to make up for the prayers you performed after you performed ablution and touched your child's private parts.
Allah knows best.