The short answer is that your wife can be served by something called substituted service. That means that you have to get court permission to serve her by FedEx or TNT. It can be done, it's just a bigger hassle. Get an attorney to help you with this, otherwise you'll waste a lot of time. As for your immigration status I cannot give advice on that since I'm not versed in immigration law, talk to a reputable immigration attorney.
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It appears that divorce is the least of your problems ... you can't file for an H-4 if your spouse is no longer in the US, and is no longer working for the H-1B company.
You need to meet with an immigration lawyer immediately.
He/she can help you find a divorce attorney that can advise you on 'service by publication' ... a slow and expensive process.
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I assume you've immigration counsel - I only know enough to say that it sounds like it could be a bigger issue there.
You file in New Jersey. Assuming mom lived here, there's personal jurisdiction over her. Then, if she won't sign for the complaint (an "acknowledgement of service"), you have her served by a process server in India. Not sure what the mystery is about that one. If she doesn't answer after being served, you proceed via default... if you have 3 kids involved, I'm going to assume you'll be working with counsel to make sure all is done correctly.
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If your wife cooperates she can sign an acknowledgement of service in India. Otherwise an international server will do it. If you marry a US citizen you may be able to adjust status and become a LPR.
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