How Do I Collect Child Support From An Unemployed Ex Wife

My wife and I have recently divorced. We have two kids ages 10 and 7. She has moved away to Georgia to live with a soldier in the military that she is not married to. She only sees the kids about 4 times a year as she opted to leave them in my custody. She is living solely off of this man that she has moved in with because she is unemployed and living with him and his 4 kids. She has said that I can file her on my taxes in order to receive any type of refund that I may be eligible for to be able to support the kids. Other than this, she has made no offer to contribute towards, birthdays, holidays, schooling, activities or any other events that may come up in the kids lives. What I am needing to know is that in my situation, how do I receive the child support that for my kids that I am desperately in need of so that I will be able to support ALL of their needs that I have been left in a bind with due to her absence?