I have attached a document I found that details the questioning of Joshua Drake. I based my answer from this document.
Joshua Drake allows his children to work in the textile factories because of NECESSITY.
Joshua Drake only works for 2 days. He has other means of income but these are not permanent nor are they enough to subsidize the needs of the family.
Everyone in the family needs to work in order for them to satisfy their most basic needs. That is why his children also work because what they earn goes to the family coffers.
For Joshua Drake, it is preferable to work limited hours and earn lower wages compared to working longer hours but is not regularly employed.
