Does a mother's ablution (wudu') become nullified if she touches an impurity while cleaning her child?

Nullifiers of ablution do not include touching impurities. However, whoever touches an impurity is not permitted to pray until they wash it off. Sheikh Ibn Baz was asked about a doctor touching a patient's private parts, blood, or urine. He replied that there is no harm in that due to necessity, and that touching private parts nullifies ablution, unlike touching blood, urine, or other impurities, which does not nullify ablution. Rather, what has been touched must be washed.