You can agree for divorce if your husband is willing to provide you spousal support , custody of children and maintenance fir children 

You dont have to accept his proposal for divorce.

Let him file a divorce case in which you may prefer not to participate, because the exparte divorce granted in US for the marriage solemnised in India will not be legally valid.

If you don’t want divorce file petition for RCR in India 

2) seek maintenance from husband and custody of children 

He cannot force you to give divorce, you can always refuse to accept his proposal, however he being an American citizen, he may easily get divorce in that country.

However  with the proof of his second marriage , you can file a criminal complaint against him for the offences of bigamy under section 494 IPC, but you can get him arrested for this offence only when he visits India.

See if husband donot want to continue you cannot force him also he is US citizen so filing anything against.him in India shall be hardship as he cannot be summoned by Indian court.

You can take handsome amount of alimony from.him for you and children's and can divorce him and can lead peaceful life.

File FIR, but your husband is American, no application of Indian law. Can file police complaint in America of domestic violence.

His marriage with that women in not valid during your marriage. You can file FIR of bigamy also.

Dear Madam,

The wife has a right to turn down a divorce; she can refuse to divorce even after filing a petition for divorce through mutual consent. Following this, the court will typically dismiss the petition for divorce through mutual consent.

In such a case, as the husband wishes to divorce, he will have to separately petition to the court to grant the divorce. Such a petition can be made by the husband only on certain grounds, listed below.

The court will call upon the husband to prove the ground sought by him for the divorce; the wife will be called to disprove the allegations. If the husband's allegations are proved, the court would award a divorce, even if the wife does not wish to divorce. If the allegations are found unsubstantiated, the court will dismiss the divorce petition.

First legality of your marriage needs to be established. If your marriage is legal then his marriage with that girl is illegal. you can go ahead with bigamy procedure also if required

No one can force you to give divorce. You can exercise your rights and file before the court for reliefs like maintenance, residence, compensation etc from your husband. 

If you are not willing for divorce nobody can force you for that. Consult with an advocate and file a case before the Family court where you reside for the restitution of conjugal rights

Don't sign any paper instead file case against him of bigamy and get the maintenance from him or lumpsum amount if he wants divorce from you.

You should file suit for alimony and distribution of properties as per US laws against your husband in case he wants divorce he will liable to pay you maintenance and alimony if he want divorce from you. 

Dear Madam,

You have to consult local lawyer as you have to file a divorce in that Country only.