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, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
The bride’s father is the one who is responsible for conducting her marriage contract and no one else may give her in marriage as long as the father is eligible for this duty as a guardian and as long as he does not prevent her from marrying (a suitable groom). If your father is a Muslim, he is the one who should conduct the marriage contract of his daughter, even if he was a Faasiq (immoral) person, because according to the preponderant opinion, the guardianship of a Faasiq father over his daughter is valid, as underlined in Fatwa 120675.
You should know that your father has the right for you to be dutiful towards him and treat him kindly and compassionately, regardless of his immorality, impiety and inequitableness. Allaah, The Exalted, commanded children to keep the company of their non-Muslim parents with appropriate kindness even if they order them to disbelieve in Allaah. Please, refer to Fatwa 88120.
Also, it should be noted that you have to maintain good ties and establish good rapport with your relatives, including your paternal uncles and aunts, even if they are immoral and treat you inappropriately; please refer to Fataawa 82279 and 85794.
One of the greatest manifestations of dutifulness towards your father and keeping good relations with your paternal uncles and aunts is to enjoin them to do good, forbid them from doing evil, and help them to return to Allaah in repentance and adhere to the path of obedience to Allaah. However, it should be noted that enjoining your father to do good and forbidding him from evil should be done in a kind and courteous way.
As for your question regarding Ghusl (ritual bath), the Ghusl is valid only if the whole body is washed with water, unless there is a valid and Sharee‘ah-acceptable excuse such as suffering harm if water is applied to the body or parts of it. In fact, what you have mentioned in the question is not a considerable harm. Therefore, you should wash your hair along with all of your body during Ghusl. If washing your hair causes it to become dry, you are advised to consult a specialist to seek treatment for that problem. For more benefit, please refer to Fataawa 82245 and 86534.
Allaah Knows best.