Fraud by NRI husband

Although I hardly advise anyone for indulging in criminal litigation against the deserting husband, but in your case as this man has deserted you in India and skipped to USA, you should file Police Complaint against him for cruelty, domestic violence and seek impoundment and cancellation of his passport. Force upon his deportation through Court to settle the criminal complaint against him and not allowed to leave the country till the matter is finally settled. The divorce even if that has to be done need to be proceeded by the settlement of permanent alimony. The Government of India is also proposing the action against the NRI wife-deserters. The link will be of help to you : https://www.msn.com/en-in/news/newsindia/nri-wife-deserters-may-lose-passports/ar-AAs6wrm?ocid=sf 

The criminal procedure has been rightly suggested hereinabove.  However, if you do not wish to go down that path, you can also file an NC against your husband putting on record these brief facts mentioned hereinabove in the local Police station of the area where you presently residing.  

I would firstly, however, advise you to build a record before proceeding on cases.  So firstly start by writing emails to your husband, putting on record his desertion of you and asking him to renew your dependent H-4 visa. You can also address his family members in the said emails. 

I would like to understand why do you wish to initiate proceddings only in the USA? Since your in-laws' are based here and so is your husband's property, it would be more beneficial for you to start proceedings here.  If you however insist, you can always approch the legal aid there.  

Yes, he has to come.  He may file an Application for exemption of personal appearance but even then, you can insist on his presence during the stage of evidence. Take copies of the notice sent by woman's cell and send your emails also.