Divorce with Mutual consent with two kids

Hi, I am married for 13yr(almost ) and having two kids (8yr old girl is indian citizen and 2yr old boy is US citizen ) we got married in India ( married is not registered) We stay in US. Me and my husband are having hard time to stay together and to manage things, as we have different upbringing and are from different cast ( ours was a love marriage) although we tried our best to forget our differences and stay together. Recently i found that my husband is having an extramarital affair ( not sure since when) and its hard for me to take it, effect of that affair is showing on our relationship and kids are getting affected. I am on H4 visa (dependent) i am not working. I have spoken to my husband of getting divorce with mutual consent and he said he will think about it ( i guess almost ready for it) what are my options, i dont have a very strong financial background or any kind of support from my family or from in laws. Can i get custody of both of my kids...?? Will i be able to get compensation till i find a job for my self...?? We dont have any property or any joint bank account on our name. If i want to continue with this relationship what are my options, for sake of my kids future as I don't have any support.