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.