1) It is acceptable for women and families to mourn their dead. However, Islam prohibits us from being excessive in our mourning/crying on the dead. Many Arab tribes had a habit/custom of having their women mourn publicly and loudly for prolonged days. The women would tear their clothes and beat themselves. They would basically make a public scene out of it. This reached a point where they didn’t show any patience, and it’s as if they rejected Allah’s will. Believers should never mourn like this. We should never lost patience and reject Allah’s will.
It seems that this what happened with that tribe. The Imam rebuked the leader of the tribe for allowing this. He basically was teaching him that sour public mourning is inappropriate (women wailing inappropriately before men and making a scene). So the Imam wasn’t prohibiting women from mourning, but he was teaching them that such excessive mourning is inappropriate, and the men had to take action to stop this Jahili practice.
2) A- The women of Ahlulbayt (a) wanted to raise awareness about the injustice of Yazid by mourning the martyrs of Karbala. Their mourning was purposeful.
B- Those women did not purposefully mourn. They mourned out of the Jahili tradition that existed in those tribes.
C- The women of Ahlulbayt did not object to Allah’s will in mourning the martyrs, whereas these women mourned in a way that signaled their impatience.
D- The women of Ahlulbayt appropriately mourned, whereas these women made a big scene in front of men.