Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Wudu (ablution) is not invalidated by cleaning a child’s urine or washing his diaper, because touching najasah (impurity) does not invalidate wudu, but it is essential to wash off the impurity if one wants to pray.
Answering your question, the Fatwa Center at Islam Q and A, states:
Touching medical equipment or the floor of the washroom barefoot does not invalidate wudu, but if there is any impurity on the floor and a woman or man steps in it, they must wash their feet if they stepped in it when it was wet, or if there is any wetness on the foot.
Touching a child’s clothes that are wet with urine does not invalidate wudu, but the one who touched it when it was wet has to wash his hand. The same applies if it was dry but his hand was wet – he has to wash his hand.” (Fatawa al-Shaykh Ibn Baz, 10/139)
As for touching blood, urine and other impure substances, that does not invalidate wudu’ but he must wash off whatever gets onto him. (Shaykh Ibn Baz, 10/141)
Shaykh Ibn `Uthaymeen (may Allah have mercy on him) was asked about a woman who washed her child when she is in a state of purity. Does she have to do wudu?
“If a woman washes her child, boy or girl, and touches the child’s private part, she does not have to do wudu, rather she only has to wash her hand, because touching the private part without desire does not necessitate wudu.
It is known that when a woman washes her children, desire does not even enter her mind, so if she washes her child, she only needs to wash her hands to get rid of any impurity that has got onto them, and she does not have to do wudu.” (Majmu` Fatawa Ibn `Uthaymeen, 11/203)
Almighty Allah knows best.