What is the ruling on a girl allowing her family to take a portrait of her and hang it on the wall of the living room, which is frequented by strangers, knowing that refusing to do so may cause distress to the family?

Photographic imaging of animate beings falls under the general prohibition of imaging. It becomes even more serious if the image is of a woman whom men might view, due to the potential for fitna (temptation/strife). The wrath of Allah is more deserving of being guarded against, for "whoever seeks Allah's pleasure, even if it displeases people, Allah will be pleased with him and make people pleased with him."