Hi KV, I’m Adv. Niharika and here is my take on your query.
s. 19 of Hindu Marriage Act, 1955 provides for multiple places where you can institute our divorce petition.
Firstly, under sec. 19 (i) where the marriage was solemnised; in lay man terms, where the marriage took place, in your case which is India. So you can file a petition at the place wherever your marriage took place in India.
Secondly, under sec. 19 (iv) where the petitioner resides at the time of filing the petition. That is to say, in case you move to India first then at the place where you will be residing in India, yup can file a petition in the court of that particular area.
Now regarding the child custody, you can file the petition where the child is residing currently (in your case, the USA) and an order from that court will be presumed to be binding on all India courts under section 14 of Civil Procedure Code, 1908.
For your convenient reading I’m attaching a few links on the Hindu marriage Act, 1955 and Civil Procedure Code, 1908. Kindly see section 19 and 14 respectively it will give you clarity.
I hope this information yields fruitful, in case of further query you can reach me at firstname.lastname@example.org