What is the process for divorce for a permanent resident?

My wife and I came to the U.S. 10 years ago and are now permanent residents, but not citizens. I am considering divorce and want to know what my rights are. I am especially worried about what my custody rights are as a dad because we have 2 daughters and my wife has threatened in the past if I divorce her she will not let me see them. What is the divorce process for residents who are not US citizens? Does a father have the same rights as a mother if she’s been the primary caregiver for the children? I would like to work with an Iranian lawyer who understands the divorce process in both the U.S. and Iran if I do have to pursue a divorce there.