Does the illness of young children or infants expiate the sins of their parents?

The illness of children is a trial for the parents, through which Allah erases sins and transgressions for them due to the worry and grief that afflicts them. The Messenger of Allah, peace and blessings be upon him, said: "No Muslim is afflicted with worry, or grief, or illness, or pain, or harm, not even a thorn that pricks him, but Allah expiates some of his sins thereby." Furthermore, the death of children and their precedence (in passing away) shields the parents from the Fire and admits them into Paradise. Scholars have mentioned that Allah causes children to suffer for the benefit that lies therein for them and for their relatives.