Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
1- Your husband does not have any right to go out or to sit alone with his female cousins. One’s cousins are not mahrams for him.
2- He also cannot do the same with your female relatives.
Responding to your question, Dr. Mohammad S. Alrahawan, Associate Professor at the department of Islamic Studies in English, Al-Azhar University, Egypt, states:
Your husband does not have any right to go out or to sit alone with his female cousins. They are not mahrams for him.
Uqbah ibn Amir reported Allah’s Messenger (peace be upon him) as saying: Beware of getting into the houses and meeting women (in seclusion). A person from the Ansar said: Allah’s Messenger, what about husband’s brother, whereupon he (peace be upon him) said: Husband’s brother is like death.” (Al-Bukhari)
The same is applicable for husband with regard to the female relatives of his wives.
Moreover, Ibn Abbas (may Allah be pleased with them) said: The Messenger of Allah (peace be upon him) said, “No one of you should meet a woman in privacy unless she is accompanied by a mahram (i.e., a relative within the prohibited degrees).” (Al-Bukhari and Muslim)
Most of our social problems come through uncontrolled mingling between male and female relatives. May Allah guide your husband to the straight path.
Allah Almighty knows best.