Dear Concern,
Please note -
01. A marriage solemnized and thereafter registered in India can be annulled only in India. Unless your marriage has also been registered in USA as per the laws of USA your case shall not be entertained in USA. Reason -
(a) You are an Indian by citizen (I am presuming this on my own),
(b) Your marriage has been solemnized as per the Hindu Marriage Act (your query mentions that you are a Hindu) and thereafter registered in India. Hindu Marriage Act is an Indian law so only courts of India will have the rights to hear any case based on this law.
02. Now coming to the question of law of validity of foreign court decree (USA in this case) then any decree passed by any competent court of foreign country is valid in India if that -
(a) court was competent to hear the matter, and
(b) court has followed the due procedure of law of that country.
03. Even if you do not participate in the case and if the sub-clause (a) and (b) mentioned in point number 02 is getting fulfilled then also the decree is valid in India.
04. An order passed by any court is valid in India if that is competent and has followed due process of law be it mutual or contested.
Having said that, see the technical ground of whether your case can be entertained in USA or not. If yes, then participate in it rather than avoiding it as the final decree will be valid in India irrespective of the fact that you have participated in that or not. If no, take objection on it and compel your husband to file for Divorce in India as per the Indian law.