Praise be to Allah, and may Allah’s peace and blessings be upon the Messenger of Allah, his family and his companions.
As to what follows:
In response to your question, we say, and with Allah Almighty lies all success:
There is no effect of this on the state of purity of wudhu. So the state of purity stays intact and is not nullified by this touch. Her touching impurity in the process of cleaning does not nullify her wudhu. And it is also not nullified by touching the child’s `awrah (private part), for if it did nullify, the Prophet (peace be upon him) would have made it clear. As for what has been narrated regarding what the Prophet (peace be upon him) said about touching the private part, “He who touches his private part should make wudhu.” This is in regards to touching out of lust, and wudhu in this case is mustahabb (recommended) by the consensus of scholars. And it has also been narrated in a hadith by Talq bin `Ali that the Prophet (peace be upon him) said, when asked about a man touching his private part, “It is only a part of you.” Meaning that a person touching his private part, or that of another person in this case, is only touching a part of his body and not touching out of lust. And this is, as in the context of the question, the case of a woman touching the private part when cleaning her son or cleaning her daughter. So there is no requisite of lust in this case, and it therefore does not nullify the wudhu, nor is it recommended to re-make wudhu. It is the same in the case if the question was about the ruling of touching najasah (impurity); does it nullify the wudhu? The answer is: No. Also, if the question was pertaining to the touching of the private part when cleaning a child and whether or not it nullifies the wudhu; the answer is: It does not nullify the wudh
Sunan Abi Dawud (181), Musnad Ahmad (7076), Sahih Ibn Hibban (1116), al-Mustadrak (474), al-Mu`jam al-Kabir (3831).
 Musnad Ahmad (4/22) (16329), Sahih Ibn Hibban (1120), Sunan al-Nasa’i (165), and graded as Sahih according to al-Albani.