Is it permissible to benefit from the work of a close relative who is a visiting domestic worker in the home without paying her a wage?

If the maid's work in your house is included in her contract with your relative and with his permission, then you are not obliged to pay her a wage. However, if her work is not part of the original contract, then she is entitled to a wage for her work, unless she worked for you voluntarily and willingly.