My girlfriend left me & moved out of state & she is not a resident there

My girlfriend and I lived in LA for 20months We have a 9 month old baby. I caught her cheating on me and she left with our baby out of state to live with her parents. When I just bought a house for us to live in this year. Now I am stuck with the mortgage and all the rest of the bills. What right do I have as a boyfriend ?
Because I LOVE my daughter just as much as she does and I want to raise my daughter too. I want to teach her ABCs and watch her first steps. It was her fault the relationship ended if it was not for her behavior we would still be together now.
Now she is calling me saying she is going to put me on child support.

My opinion is she is not mature enough to take care of our baby because this is not the first time i caught her cheating on me this is more like the third also i just found out that she is 3 weeks pregnant but this time the BABY IS NOT MINE!

My girlfriend is actually not a resident of the state of Colorado in fact she only has her green card and it is actually expired and she is suppose to go back to her country actually a few months ago border patrol or customs went to go pick her up from her moms house but she was not there she was suppose to be in school but she dropped out do you think it might be a little easier for me to get my daughter back
This is the Link to Colorado residence tell me if this is the right info i need to get my daughter back
http://galleriarealestate.com/html/colo_require.html
answers are appreciated