Could it be that Harriet was destitute and was unable to pay a debt. I notice on Ancestry that the actual sentence was for 4 days or pay 11s 2d that she obviously hadn't got. I also notice that she only served 3 days in prison. She may have worked off the debtor perhaps someone paid the 11s 2d for her. Albert was released from prison 8 December 1902. If she was indeed destitute this could be the reason for losing the children.
Jenny, if she was taken away to prison then the authorities would have to look after her children. They would have gone into the workhouse until their mother came back to look after them.
Dave