1) you can seek joint custody of the child
2) in one recent case in bombay family court granted joint custody to both parents of 8 year old child
3) actual physical custody was given to mother for 183 days and father for 182 days
4)in your case since you are located in USA it would affect child studies if she were to stay with you for 182 days .
5) you can claim custody during her summer vacations / Christmas holidays so that she can stay with you also
6) you cannot bring child to USA if you lose the custody case