What is the ruling of Islamic law regarding a wife remaining with her non-Muslim husband who refuses her entry into Islam, and what is the ruling regarding her daughters remaining in a Hindu school, and what is the ruling regarding her marrying another man while still being married to her first husband?

If the husband prevents his wife from embracing Islam and refuses to convert, and he is ill-mannered, then there is no benefit in remaining with him. It is advisable to separate from him immediately and seek custody of the two daughters to raise them as Muslims, as custody goes to the Muslim parent in cases of separation. As for the other Muslim man, you must ascertain his chastity and the soundness of his faith, and refrain from any relationship with him before marriage. If these conditions are met, then it is advisable to marry him after the expiry of the prescribed waiting period (iddah) from your current husband. And remember the story of Pharaoh's wife, as stated in the Almighty's words: (And Allah presents an example for those who believed: the wife of Pharaoh, when she said, "My Lord, build for me near You a house in Paradise and save me from Pharaoh and his work and save me from the wrongdoing people").