Well, you're right about one thing at least.........that's a big mess!
The absolute best thing you could do right now is to dump the girlfriend and re-commit yourself to your family. There are lots of ways to do that, beginning with marriage counseling.
But, clearly, that's not what you
want to do. So, I won't waste your time asking you to consider it. Frankly, if you can't work up a little more human respect for your wife than what you have now, it wouldn't work anyway.
The first thing you have to do is to stop lying to yourself. You are under the impression that you were
forced into marriage and
trapped into fatherhood. Unless it was a 'shot-gun' wedding, and she was giving you mind-altering drugs to get you into her bed.......
These fallacies will alter your thinking, and you need a clear head. You are not "technically married". You are cheating on your wife. She may have done it first, but you're doing it now. So, you don't get to be a better person here. Or worse yet, a VICTIM in the circumstances of your own life.
Once you accept that you are not the 'nice guy' that you thought you were, you'll be able to move on with the next steps. (See, nice guys, don't have the stomach for taking a woman's children and home from her.)
In deciding child-custody, most courts are forbidden from taking gender into account. It is a form of discrimination. Check this site for more info on your particular state:
http://www.divorcenet.com/
The decision in many states is made based on who currently has the custody and what quality of life (and stability) they are providing to the children.
Men don't ask for custody but maybe 20% of the time, but of that small number 80% will be granted it. The trick is to setting up a stable home-life with good daycare
before the temporary custody is decided. So hire the best Nanny that you can afford, and make sure the kids stay in the home with you. Then file for Separation.
If she moves out and takes them with her you may be looking at a situation in which a 'change in circumstances' must be proved.
I have to warn you though. If your wife finds out you are cheating, it'll likely go the other way for you. This could lead to bias in the judge that is NOT surmountable, even though it doesn't signafy in the interpretation of the law.
If it's true love, than your little college girl can wait. She may need some time to mature anyway before taking on a ready-made family.
I'm sorry to sound harsh with you. It's better to slap a hand than hold it sometimes. And you'll need to very clearly define what your goals and reasons are if you're going to be successful in this venture.
Good luck to you.