Children

This is going on in thousands of families but you as a believing and God fearing person should deal with it carefully and humbly. 
You must tolerate your mother in every possible way. She is after all your mother and her right in you is greater than explaining. Even if the parents were non believers,b their rights as parents remains great in their children. Try your best to avoid instigating her by any word or act, and always tolerate her behavior and comments. It might be a test for you from Allah to examine your faith in Allah. Never react badly to any of her behavior and comments. Annoying your mother or father causes anger of Allah on you, God forbid.

Wassalam.

1. When you know that Allah does not allow any marriage between a Muslim female and a non Muslim man and you write that  "you feel that you went against Allah", you must repent and seek forgiveness and come back to Allah and never insist on doing wrong.

2. If you can convince the man and explain to him how to become a Muslim, then you need to recite a marriage agreement (Nikah) between you and him after becoming a Muslim in his heart.

3. If he refuses to become a Muslim, then there is no way that you can remain with him.

4. You must save yourself and your future from sinful acts.

Wassalam.

According to Amaali al-Shaikh al-Sadouq, Janab e Muslim ibn Aqeel (AS) had two sons martyred in the day of Ashura with Imam Husain (AS) and another two sons who ran away from Karbala after the martyrdom of imam Husain (AS). These two sons where martyred later on after Karbala and were buried near Musayyab in Iraq. أمالي الشيخ الصدوق

Wassalam.

Raising a child in need who is not your child is a great act of reward and it is a way to Paradise if it is done according to the teachings of Islam. As the child is not your child, there is no inheritance between you and the child, although you are free to give him in your will up to one third of what you leave, and you can gift him during your life whatever you like to gift him.

When the child becomes Baaligh, Hijab is must.

Wassalam.

Who said that there won't be any children in Paradise? Allah (SWT) will reunite the believers with their children in the Paradise (Sura 13, Verse 23 and Sura 40, Verse 8). In the Hadeeth that all children of the believers who die during childhood will be looked after by Sara wife of Ebraheem and will be offered to enter Paradise, they will say: No till our parents enter Paradise. This means that the children of the believers will enter Paradise with their parents.

Wassalam.

Parents are responsible to look after their children and protect them from harmful or dangerous websites and bad company. They must do whatever they can to protect their children and never leave them exposed to any harm or danger. That does not mean to insult or degrade their children but just to look after them and protect them. If they come to know about any mistake from any of their children, they must keep his respect and avoid insulting him.

Wassalam.

You need to keep in touch with her and treat her nicely being a practicing Muslim so that she will see the great manners of Islam. You should try to invite her to Islam as and when you find a suitable chance. Her being non Muslim does not mean always that she denied Islam deliberately. She might had been a victim of ignorance or misleading propaganda.

You should do your best to give the practical evidence that Islam is the best religion.
Wassalam.

Parents are not allowed to do injustice against their children or any of them. Being abusive with people is not an Islamic way to behave. Yet, if the parents or any parent becomes abusive, the children are never allowed to yell at them under any circumstance. Allah says in Quran about treating your parents: And never tell them Uff (any word of annoying) and never raise your voice at them. (17:23).

There is no question of retaliation we deal with our parents, no matter how bad might be. Even Kafir (disbelieving) parents who insist on their children to become disbelievers, must be treated in nice way. Allah says in Quran (If your parents strive to make you a Mushrik (polytheist), don't obey them, and deal with them nicely and kindly)(Sura 31, verse 15).

Wassalam.