Is it permissible to go to a shopping mall where there are women who are uncovered and do not wear the abaya, if one's family obliges one to do so?

Obedience to parents and others is conditional upon not disobeying Allah, as the Prophet, peace and blessings be upon him, said: "There is no obedience in disobedience to Allah; obedience is only in what is right," and his saying: "There is no obedience to one who disobeys Allah."

It is obligatory to advise family members gently and kindly. If it is possible to travel with them without participating in forbidden places, then there is no harm, while continuing to advise them.