I am very successful man as I am a young doctor living in London. I have everything that anybody could want and all praise is to God that He has showered so many blessings on me. Sadly, I have not been a faithful servant to God, I have a very beautiful wife and have a child who is aged 5 and daughter aged 3, but this woman to whom I am married is a Hindu. She still practices her faith. In my home I have a whole room dedicated to my religion where I pray when ever I get the chance. Also, I have a mini temple area where my wife prays. A few days back I and my wife were discussing my children’s religion she wants them to be brought up in both faiths in Islam and in Hinduism respecting both ideologies. She (my wife) has taught my son some Hindu prayers and I try and do my best to teach him Muslim prayers. Currently I was attending a Medical conference in Switzerland and on my return home I witnessed that my son was praying Muslim prayers in front of the Hindu gods. As I asked my son what are you doing he replied I am praying to ALLAH. This event confused me a lot and got me thinking that would it be acceptable for my children to be brought up in both religions respecting both beliefs?
Insha Allah I hope to hear from you soon

 Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Allah forbade the Muslim to marry Kafir (non Muslim) women other than  the chaste women of the People of the Book. This means that it is not permissible for a Muslim to marry a Kafir woman except if she is a Christian of a Jew and she is chaste. Thus, it is not permissible to marry a Hindu woman. Allah says: "And do not marry Al-Mushrikât (idolatresses, etc.) till they believe (worship Allâh Alone). (Al-Baqarah 2:221)

Therefore if you knew that it was forbidden, and despite this fact you married her, then you have indeed committed a major sin. You have to repent from this sin by divorcing her, because your being with her is fornication (Zina), and your children are children of Zina, and they shall not be named after you.

Nevertheless, if you did not know that it was forbidden to marry her, this marriage is still not valid and by staying with her you are committing adultery. You have to divorce her immediately. If she becomes a Muslim, then you can marry her after that.

However, the children you had with her will be named after you in this case. Sheikh Al-Islam Ibn Taymiya said: "All the Muslims agree that any marriage in which the husband believes that it is a correct marriage, and there is sexual intercourse between that husband and his wife, the children therein will be named after the husband, and they inherit each other according to the consensus of the Muslims even if the marriage is invalid in itself, whether the husband married a Muslim woman or a Kafir one."

You have to take your children from her, teach them Islam and bring them up according to Islamic teachings, and be very careful not to lose them. Prophet (Sallallahu Alaihi wa Sallam) said: "whomever Allah makes a guardian over any trust, and he dies while cheating his trust (not fulfilling the rights of the people he is trusted upon, then paradise will be forbidden for him" reported by Muslim.

You have to be steadfast on offering your obligatory prayers, as they are the most important practical pillars of Islam. However, there is a difference of opinion about a person who does not perform the prayers whether he is a Muslim or a Kafir.

If you wish to get married, then choose a religious Muslim woman according to the advice of the Prophet (Sallallahu Alaihi wa Sallam), she will help you in bringing up your children, and if you die, she will bring them up according to the teachings of Islam.

Allah knows best.