Wa `alaykum as-salamu wa rahmatullahi 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.
Dear brother, we commend your eagerness to become well acquainted with Islam and its teachings and also your eagerness to keep your children stick to Islam’s teachings.
It is the duty of parents to raise their children upon the teachings of Islam by using all possible good means. In fact, the Internet can help parents in this regard if it is used correctly. However, parents should guide their children to the ways of using it in a positive way and protect them against misusing this service.
In response to your question, the prominent Muslim scholar, Sheikh Muhammad Iqbal Nadvi, Imam of Calgary Mosque, Alberta, Canada, and Former Professor at King Saud University, Riyad, Saudi Arabia, states,
There are many ways of protecting both children and ourselves from the haram (unlawful) as follows:
1- By creating a barrier between us and sins.
2- By providing alternatives to take us away from the haram.
Applying this to your situation, you need to establish firm and healthy channels of communication with your children and explain to them the Islamic position concerning these issues and how to deal with them. The best way to achieve this is to be a good role model for your children, for if they see you as a good example, they will learn the good from you as well.
You are supposed to introduce alternatives to them. There are many good Islamic websites that they can visit and learn from. They can be given tasks to do on each website, and then can receive prizes for that.
Most importantly we must teach our kids how to choose the right friends, who are aware of Islamic teachings and can protect them from learning about haram.
The following are some a Qur’anic verses and hadiths:
1- Surat An-Nur 24:30-31
2- Surat An-Nur 24:19
3- Surat An-Nur 24:21
4- Surat An-Nur 24:27, about the manners of family life.
5- Surat An-Nur 24:58-59
1- “The eye does commit zina (adultery or fornication) and its zina is the lustful look..”(Al-Bukhari and Muslim)
2- “A man must not look at the `awrah (parts to be covered) of [another] man and a woman must not look at the `awrah of [another] woman; and they shall not share the same blanket when sleeping in the same bed.” (Muslim)
Allah Almighty knows best.