What is the ruling on allowing sisters to go out to the the marketplace without a mahram, with the mother present and the father's knowledge, even though their going out is not out of necessity? And is there a sin upon whoever allows them to go out?

A woman is religiously commanded to stay in her home and not go out except for a necessity, based on the Almighty's saying: "And abide in your houses and do not display yourselves as [was] the display of the former [time of] ignorance," and the Prophet's (PBUH) saying: "Woman is 'awrah, so if she goes out, the devil beautifies her in the eyes of men." Her going out for a necessity must be with adherence to Islamic manners, such as not displaying herself or wearing perfume, and the destination must be safe; otherwise, a mahram (definition) or a trustworthy mother must accompany her. There is also a prohibition against a woman traveling without a mahram.