All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is not permissible for a man to marry a woman who is already married (currently has a husband); and it is also not permissible for your father to marry this Hindu woman even if she is not married, as it is Islamically forbidden for a Muslim man to marry a disbelieving woman who is not from the People of the Book (i.e. not a Christian or Jew); Allaah says (what means): {And do not marry polytheistic women until they believe...}[Quran 2:221] For more benefit, please refer to Fatwa 87895.
Therefore, he should be advised and it should be clarified to him that what he has done or wants to do is wrong, and he must repent to Allaah from this illicit relationship. For more benefit on the conditions of repentance, please refer to Fatwa 86527.
Your mother's agreement or objection are of no consideration as long as it is impermissible for your father to marry that woman. Likewise, her agreement has no consideration for him marrying a woman who it is permissible for him to marry, such as a Muslim woman who is not married, unless your mother stipulated a condition in the marriage contract that he does not take another wife with her.
Allaah Knows best.