Praise be to Allah.
In your question you said that your father married a Hindu woman and made her become Muslim. If the marriage contract was done when she was a Hindu, and she became a Muslim after that, then the marriage is invalid, and your father should do a new marriage contract, because Allaah has forbidden Muslim men to marry mushrik women until they become Muslim. Allaah says (interpretation of the meaning):
“And do not marry Al-Mushrikaat (idolatresses) till they believe (worship Allaah Alone)”
If the marriage contract was done after she became Muslim, then the marriage is valid.
It is not permissible for your father to marry a woman who is as you describe. Islam encourages marriage to religiously-committed women. Her dressing in a provocative manner prevents the Muslim from making this choice. You have to advise your father in the way that is better to urge her to adhere to Islamic rulings, which includes telling her to wear hijab and behave in a proper manner.
The Messenger (peace and blessings of Allaah be upon him) encouraged marriage to women who are fertile. It was narrated that Anas ibn Maalik (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) used to say: “Marry the one who is loving and fertile, for I will feel proud of your large numbers before the other Prophets on the Day of Resurrection.” Narrated by Ahmad (12202). Classed as saheeh by Ibn Hibbaan (3/338) and by al-Haythami in Majma’ al-Zawaa’id (4/474).
Sham al-Deen Abaadi (may Allaah have mercy on him) said:
Wudood (loving) means she loves her husband.
Wulood (fertile) means the one who bears many children.
These two conditions are mentioned together because if a fertile woman is not loving, her husband will feel no desire for her, and if a loving woman is not fertile, the desired aim will not be achieved, which is to increase the numbers of the ummah by producing many children. These two characteristics may be known in the case of virgins from the behaviour of their relatives, because in most cases relatives are similar in behaviour and characteristics.
‘Awn al-Ma’bood (6/33-34)
The Prophet (peace and blessings of Allaah be upon him) told men not to marry infertile women. It was narrated that Ma’qil ibn Yasaar (may Allaah be pleased with him) said: A man came to the Prophet (peace and blessings of Allaah be upon him) and said: I have found a woman who is of good lineage and beautiful, but she cannot have children. Should I marry her? He said: No. Then he came to him a second time, and he told him not (to marry that woman). Then he came to him a third time and he said: “Marry the one who is loving and fertile, for I will be proud of your great numbers before the nations.” Narrated by al-Nasaa’i (3227) and Abu Dawood (2050). Classed as saheeh by Ibn Hibbaan (9/363) and by al-Albaani in Saheeh al-Targheeb (1921).
This prohibition does not mean that it is haraam, rather it is makrooh. The scholars stated that choosing a fertile woman is mustahabb, not obligatory.
Ibn Qudaamah said in al-Mughni:
It is mustahabb that she be from a family whose women are known to bear many children. End quote.
Al-Manaawi said in Fayd al-Qadeer (6. hadeeth 9775):
Marrying a woman who is not fertile is makrooh. End quote.
Just as it is permissible for a woman to marry an infertile man, it is also permissible for a man to marry an infertile woman.
Al-Haafiz said in al-Fath:
As for one who cannot have children or who has no desire for women or for intimacy, this (marriage) is permissible in his case, if the woman is aware of that and agrees to it. End quote.
With regard to your father’s wife giving her sons Muslim names and putting them in an Islamic school, these are good things that your father has done. Changing bad names or foreign names to Arab and Muslim names is a good thing. See the answer to questions no. 23273, 14622 and 12617. Putting them into an Islamic school is a means of introducing them to true Islam and convincing them of it, and we hope that they will become good Muslims.
You have to honour your mother and take care of her, and advise her to give your father his rights. It is not permissible for her to go against his command unless he tells her to do something that is disobedient to Allaah. You should also advise your father’s wife and show her the way to do good. You should pay attention to her sons and help them to get to know Islam and follow its rulings.
We ask Allaah to set your family’s affairs straight, and to guide you to obey Him, and help you to worship Him properly.
And Allaah knows best.