Firstly, you cannot indulge in forum shopping in this manner. When you have already approached the US Court, then, until and unless you withdraw the same, you cannot approach Indian Courts. Proceedings for execution of Foreign Decree is different and in any case, the same will not apply to the present case.
Secondly, are you seeking guidance for yourself or your wife as you have mentioned " Or my wife should be in India to file the divorce and serve the papers? It is best advisable that the both of you reach a consensus and agree for Divorce by Mutual Consent.
Also kindly specify Where were you married? Where were you and your wife based at the time of marriage?