Does a child's vomit on one's garment invalidate wudu' and nullify prayer if performed with that garment, and does the continuous cleaning of children from feces and urine invalidate wudu'?

The majority of jurists hold the view that vomit is impure. Therefore, if a child vomits on clothing or the body, the affected area must be washed. The mother's ablution (wudu') is not invalidated by this, nor by touching the child's urine or feces; however, she must wash off whatever has come into contact with her body or clothes. As for the invalidation of ablution by touching the child's penis or the female child's private parts during cleaning, this is a matter of scholarly disagreement, but the fatwa (definition) here is that it does invalidate ablution.