I would say that there is not much of a difference between leurs (not leur because of the plural) and les. In this context where he talks to the big families of Ireland, both of them indicate that the children that would be eaten are their own children.

If you used des, we would lose the meaning of the sentence and it would not necessarily imply the children of those families.

If it hadn’t been mentioned that he talked to the big families, leurs would have been more correct than les or des.