1. You can negotiate with your husband to jointly file a mutual consent divorce petition on agreed terms allowing you the sole custody of your daughter, which will be disposed of within 6 & 1/2 months from the date of its filing.
2. If he agrees with your above term, you can get the MCD petition sent to you at USA and sign and notarise the same before the appropriate officer of the local Indian Consulate for returning to him for filing before the Indian Court.
3. You shall have to appear only once before the said Court after 6 months during the 2nd motion to confirm that you still want the divorce.
4. I shall not consider it prudent on your part to allow any case proceed ex-parte including divorce and child custody case.
5. Since you are a Citizen of the USA, you can file a divorce suit before the USA Court and also file an application for child custody for her welfare which you are likely to get.
6. As per the Apex Court Judgement, a child having American Citizenship can not be kept away from his/her Country and also from his/her father/mother staying in that Country being its citizen.