I was married in India under HMA and divorced in US. Please reach out to me via pm.
Without knowming much about the case ( which US State are you in - we have laws per State. Do you have children with her ? Is there US property ? ) background and although not authorised to practice law in US or in India, I can make the following suggestions:
1. Apply for Dissollution of marriage on the grounds of "irreconciliable differences".
2. Serve the papers to her in India. I think there is a legal clause which says that she has to be a resident in that county for more than 6 months before you can file/serve. US court will dissolve Indian marriage and give you a decree.
3. In the dissolution motion, depending on the State, you can ask for 100% of property, funds etc AND 100% full custody. OR you can be humane and give 50-50 of everything. For children, that would amount to joint legal and joint physical.
4. Everything that you have aquired since marriage is community property and can be split 50-50. If the property is in India and if you can prove it, US court will ask that the property be split - compliance of this is perhaps debatable.
5. You can get the US court to order your wife to pay you alimony and pay you child support if you have the kids. You will have to prove that she is working. Law is - you can get alimony for 50% of the length of marriage. If she does not comply, you can file contempt of court and make it a criminal matter.
6. DV - Any DV element you throw into the case, you become the undisputed King. You get several benefits from the State government and several free services from the county. DV will help you get your green card faster and some of the fee is waived.
7. Re-marrying. You will need your divorce decree before you re-marry. When you are marrying in US, you first apply for marriage license, in that, you have to declare your previous marriages. Also, when you are filing Green Card ( forms I -130, Form I-485 for adjustment of status), you have to provide proof of termination of previous marriage.
8. Kids - Do you have kids. If yes, and if they are in India, do declare the exisitance. You cannot file for divorce and not disclose the exisitance of kids. Remember, the kids may be physically present with her in India but you can get full physical and full legal custody. There are tax implications and benefits for you here.
9. Within 3 months of marrying US citizen, you will get your EAD ( work permit) and within another 3 monthset you will get your GC. You can then file for your childrens GC if you wish and bring them to US.