Firstly: 

We ask Allaah to help you to do good, and to make things easy for you and relieve you of your distress. For what a Muslim woman hears and sees of those who have turned away from the religion of Allaah or whose commitment has become very weak, she has to bear that with patience and seek reward for things that she suffers. She had to have hope in her Lord and ask Him to help her to remain steadfast. 

It is not permissible for her to respond to their demands or to go along with their whims and desires for her to mix with them, look at them, shake hands with them and give up hijaab, because if she pleases them in this manner she will incur the wrath of her Lord. 

Secondly: 

The sons of your husband’s brothers and sisters are not mahrams, rather they are among the people of whom you should be extra cautious, because the Prophet SAWS (peace and blessings of Allaah be upon him) likened them to death. 

It was narrated from ‘Uqbah ibn ‘Aamir that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Beware of entering upon women.” A man from among the Ansaar said, “O Messenger of Allaah, what about the in-law?” He said, “The in-law is death.” 

(Narrated by al-Bukhaari, 4934; Muslim, 2172) 

Al-Nawawi said: The scholars of Arabic language are agreed that al-hamu (translated here as “in-law”) refers to the relatives of a woman’s husband, such as his father, paternal uncle, brother, brother’s son (nephew), cousin (son of paternal uncle), etc. Akhtaan (sing. khatan) refers to the relatives of a man’s wife, and ashaar (sing. suhr) refers to both.

 With regard to the Prophet’s words “The in-law is death,” what this means is that there is more fear with regard to him than anyone else, and evil is to be expected of him, and the fitnah (temptation) is greater because he is able to reach the woman and be alone with her without anyone denouncing that, unlike the case of one who is a stranger. What is meant by “in-law” (hamu) here is the relatives of the husband apart from his father/grandfather and sons/grandsons. Fathers/grandfathers and sons/grandsons are mahrams for his wife and it is permissible for them to be alone with her. The word “death” here does not refer to them. Rather what is meant is the brother, brother’s son, paternal uncle, cousin, etc, who are not mahrams. People are usually careless about this matter and a man may let his wife be alone with his brother. This is what is referred to by “death” and should be prevented more than her being alone with a stranger for the reasons mentioned above. What we have mentioned is the correct meaning of the hadeeth. 

Sharh Muslim, 14/154 

Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allaah have mercy on him) said: 

It is permissible for a woman to sit with her husband’s brothers or cousins, etc., if she is wearing complete shar’i hijaab, which means covering her face, hair and entire body, because she is ‘awrah and fitnah. That is if there is nothing dubious about the gathering. But if the gathering is one in which there is something dubious, then it is not permitted, such as sitting with them in order to listen to singing and musical instruments, etc.; and it is not permissible for her to be alone with any one of them or with anyone else who is not a mahram for her, because the Prophet (peace and blessings of Allaah be upon him) said: “No man should be alone with a (non-mahram) woman unless she has a mahram with her.” (Saheeh; agreed upon). And he (peace and blessings of Allaah be upon him) said: “No man should be alone with a (non-mahram) woman, for the third one present will be the Shaytaan.” (Narrated by Imam Ahmad with a saheeh isnaad from ‘Umar ibn al-Khattaab. May Allaah be pleased with him). 

And Allaah is the Source of strength. 

Fataawa al-Mar’ah al-Muslimah, 1/422, 423 

Thirdly: 

As for a woman shaking hands with a non-mahram man, this is haraam. It is not permitted for you to take this matter lightly just because your relatives or your husband’s relatives want you to. 

It was narrated from ‘Urwah that ‘Aa’ishah told him about the bay’ah (oath of allegiance) given by the women: “The hand of the Messenger of Allaah (peace and blessings of Allaah be upon him) never touched the hand of any woman. When he accepted the oath of allegiance from a woman, he would accept her words and then say, ‘Go, for you have sworn your allegiance.’”

(Narrated by Muslim, 1866) 

So this infallible one, the best of all mankind, the leader of the sons of Adam on the Day of Resurrection, did not touch women, even though the bay’ah or oath of allegiance originally was done by giving one's hand. So the ruling should be even more strict with regard to other men?  

It was narrated that Umaymah the daughter of Raqeeqah said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “I do not shake hands with women.”

(Narrated by al-Nasaa’i, 4181; Ibn Maajah, 2874; classed as saheeh by Shaykh al-Albaani in Saheeh al-Jaami’, 2513) 

Shaykh Ibn Baaz (may Allaah have mercy on him) said: 

Shaking hands with women with a barrier in between is something that is subject to further debate, but the view which is most likely to be correct is that it is not allowed at all, based on the general meaning of the ahaadeeth, because the Prophet (peace and blessings of Allaah be upon him) said, “I do not shake hands with women,” and so as to ward off the means (that may lead to immoral actions). And Allaah knows best. 

Haashiyat Majmoo’ah Rasaa’il fi’l-Hijaab wa’l-Sufoor, 69. 

And Allaah knows best.