Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Islam legislated marriage for the achievement of great religious purposes, the most important of which is the stability of life.
Allah says: " And among His Signs is this, that He created for you wives from among yourselves, that you may find repose in them, and He has put between you affection and mercy. Verily, in that are indeed signs for a people who reflect." (Ar-Rum 30:21)
So, both of the spouses have to make their effort to achieve this. If any problem that hinders their life happens, they have to resort to the Shariah to solve that. The husband has to help his wife establish good relations with her kinship in kindness, and should recognize his in-laws rights on him, and he has to do his best to be kind with them.
However, it is obligatory on the wife to obey her husband. If the latter prohibits his wife from visiting her family, she has to obey him. This obedience becomes more obligatory if the visit contains a Haram thing or causes any harm.
But ordering his wife to visit his relatives and mix with them in a way that causes temptation, is not permissible, she does not have to obey him, because there is no obedience to a creature in disobeying the Creator.
Anyway, we advise you not to interfere with what is going on between your sister and her husband in matters like those mentioned in the question. Because it is more appropriate for the husband to look into the interests of his wife, especially that she is patient about what could happen to her from his side and bears his shortcomings.
However, you have to advise him about his mockery about some people, and about his causing some trouble. This is his right on you as a Muslim.
The prophet said: "Religion is advice," reported by Muslim.
Allah knows best.