Hello,
Both spouses are Indian citizens. Marriage took place in india under hindu marriage act. I initiated divorce proceedings and she responded and agreed. Both were working here but wife's visa expired during divorce proceedings. Wife along with the child who is being supported and is a US citizen, was permitted to relocate to India for 15 Months with an undertaking under oath to return to US thereafter and also to register the judgement and order with all authorities in US and India. US Court retains Jurisdictions over the parties irrespective of the countries of domicile, In between divorce decree granted by US court.
Upon expiry of the permitted relocation period and without complying with stipulation in the court's order, ex-wife is evading return to US and also holding the child outside US boarders beyond the permitted period.

My question is : -
What are the grounds on which US court can terminate child support and also retrieve the child ?

Get an attorney on this one.

My guess (albeit an educated guess) is that if a US court issued a court order requiring the return of the child to the US and the mother is in contempt of that order, a request could be made to find her in contempt and order a warrant for her.

But even if the court orders the return of the child, I don't see them trying to compel the Indian government to compel return of the child.

As for terminating support, NY law keeps support and visitation separate. So the non return of the child is unlikely to affect support.

Get an attorney on this one.

My guess (albeit an educated guess) is that if a US court issued a court order requiring the return of the child to the US and the mother is in contempt of that order, a request could be made to find her in contempt and order a warrant for her.

But even if the court orders the return of the child, I don't see them trying to compel the Indian government to compel return of the child.

As for terminating support, NY law keeps support and visitation separate. So the non return of the child is unlikely to affect support.

Agree!
The United States of America is not declared as a "reciprocating territory" by the Government of India and thus American Court orders CANNOT be enforced in India.