Need divorce from my cheating husband and custody of our daughter

Assuming you are a Hindu  you will be governed by the Hindu Marriage Act 1956.

If you are unhappy with the marriage, you have two option available with you. Either you can file a contested divorce under Section 13 (1) on grounds of cruelty. Along with the said petition you can file an application for maintenance under Section 125 of Crpc. Furthermore, you can file another petition with respect to the custody of your children. If your daughter is a minor then you need to file a petition for the custody of the daughter. 

Section 6 of The Hindu Minority and Guardianship Act states that the ‘natural guardian of a Hindu minor, in respect of the minor’s person as well as in respect of the minor’s property …. in the case of a boy or unmarried girl is the father, and after him, the mother, provided that the custody of a minor who has not completed the age of five years shall ordinarily be with the mother. For appointment of declaration of any person as guardian, the court shall consider the welfare of minor. The welfare of the child is determined neither by the economic affluence nor a deep mental or emotional concern for the well being of the child. The answer depends on the balancing of all these factors and determining what is best for the child’s total well being."

The above mentioned procedure is one option. 

The other option available for you is to file a Mutual Consent divorce under Section 13 B of Hindu Marriage Act 1955. But this is only possible if your husband is willing to give you a divorce as well. So you will have to enter in a MOU /agreement with your husband wherein you will have to specify the terms of your divorce such as alimony/maintenance and custody of your children. This process is faster and cost effective.