A sister is a female sibling.
It is allowed and he would probably be happy about the marriage, however, it is understandable if the family wishes to postpone it. Also, some cultures have viewpoints about these things (which are not specifically prescribed by Islamic law but could be taken into consideration although it is not required to adhere to cultural viewpoints).
1. Many persons who claim to be atheist do so with out real thinking but just for psychological reasons like to oppose the family or the atmosphere or to look like different or to show that they are modern ,etc.
We should not take their claim as a studied intellectual decision, unless we discuss with them in neutral atmosphere with out any challenge or instigation.
2. If you are sure that a person has become an atheist, you should look at the reasons and try to understand the background of the situation.
3. We need to see and assess his arguments and the authority which he believes in, e,g. Intellect or reason, or science etc. We must talk to him in the language which he understands. Those who claim believing in logic and reason, should be given evidence based on logic and reason. We as followers of the Real Islam of the Prophet (SAWA) and Ahlul Bayt (AS) have the richest treasure of intellectual and logical evidence.
4. Invite them for dialogue and debate based on what they claim to believe in and be patient and tolerant.
5. Never expect them to accept your evidence right away. They might reject it verbally but keep thinking about it for sometime. Give them the time which they require and keep on presenting the evidence now and then in a polite and respectable way.
6. If an atheist invites other to be like him, you can keep logical principles and rational thinking as your weapon to easily refute his claims and proof him wrong. Never insult nor attack him but counter his argument with logical and rational evidence with etiquette and respect.
7. If the person respects noble personalities like the Prophet Muhammad (S) or Imam Ali (A) or Imam Husain (A), you can remind him with life and sayings of these great leaders who had the maximum level of intellect.
8. Always keep the doors open for dialogue and never lose hope. No one knows when the heart and mind will open and becomes able to see the truth.
Your wife has misunderstood the Islamic rule in this matter. Mahram is the person who is permanently forbidden for marriage with her under any circumstance for life e.g. her real brother , real uncle, real father, father in law, her son and son in law. Her sister's husband is not permanently forbidden to marry her, but only when her sister is his wife. If she dies, God forbid, or if she is divorced from him, marriage will be then allowed between this man and any of the unmarried sisters of his ex-wife.
Her sister's husband is not Mahram at all and must observe full Hijab in front of him like any other non Mahram man.
It is very important for your respected wife to educate herself about the definition and rulings related to maḥram/non-maḥram cases.
Unfortunately she is misinformed, and has only half of the facts correct.
In Islam, a man cannot marry two sisters at one time, but this does not mean that the wife's sister becomes maḥram to the husband, nor does it mean that the sister's husband becomes maḥram to the wife's sister.
So, although he cannot marry his sister's wife as long as he is married to his wife, it still does not mean that she becomes maḥram to him.
It is still haram for him to see her without hijab, or look at her with lust, or shake her hand, or be alone with her, and so on.
This is a view that all our jurists have.
As for the case of her staying at their home, if all other shar'i matters are observed, yes she can.
And Allah knows best.
If you not interacting with them or limiting interaction with them can prevent further animosity and problems, then it may be necessary to take such steps. It may also be advisable to keep a distance away from such people if they are being unjust and rude towards yourself. Of course one should try keep good manners and not stoop to the level of those who are being rude. But it still isn’t obligatory upon you to have a relationship with them.
May Allah grant you success
One cannot force anyone to accept the truth rather the important point is that you put the proof upon her. If she refuses to hear anymore out of stubbornness, then you’ve done your job and have no blame. Those who are stubborn should be left if one sees that there is no benefit in utilising anymore time with them.
Furthermore it is not recommended to take an approach where they feel that you are trying to force them. Usually the ‘overly pushy’ type of approach makes people further away from religion.
The best approach to take would be one combined of showing good ethics and respect. Know that helping one to the path of guidance can sometimes take years. Therefore, always have hope that she may take interest in future and come to you for knowledge.
There will always be a time in someone’s life where they think about God; this may occur due to a particular incident such as a death of a loved one or near death experience. It is however upon the person to go deeper and search.
Also the below verse is something for us all to take into consideration when trying to propagate our faith.
“Call to the way of your Lord with wisdom and goodly exhortation, and have disputations with them in the best manner; surely your Lord best knows those who go astray from His path, and He knows best those who follow the right way.”
May Allah grant you success and guide your sister to Shia Islam.
Yes, it is permissible if there is compatibility in Fath and Akhlaq.
You are responsible about your father. Do not miss this great chance to serve him in his old age and do not listen to any one including your wife if she wants to discourage you from serving your father.