Effectively, children have always been involved in labor - the difference of the Industrial Revolution was that children were laboring separately from their parents, who might have some modicum of attachment to their safety and health.

Specifically for mining:

Children were used in mines because they are smaller. This meant that the tunnels inside the mountains didn't need to be so big. Since removing the material was a big undertaking of manual labor before the use of explosives and other modern tools, one reason why children were used waa in order to lessen the necessary workload.

And in addition: children labour was the norm for the majority of the past. Childhood as a separate part of life without work (older than 5 years or so) is a pretty modern context. At least for the majority of people. Powerful families had different dynamics, as always.

They yearn for the mines