I am really sorry to hear about what you've got going on. Glad she went to her parents' house, so you know the kids are safe.
Don't mean to play devil's advocate here, and I can't really tell anything since I don't know how old y'all are. How long y'all have been together, etc.
I will tell you that postpartum depression is a clinical term for something that may have ties to an imbalance in body chemistry. Having a baby at any time in life is just a tad bit tiring. Has she seen a doctor?
Communication - call once a day, just to check on the kids, diapers, formula, offer to help out. Send her an email, tell her you just want to check on the kids. Offer to take the kids for a day, or something like that. Offer to take them to the doctor's, there's a checkup due for the newborn.
Here's the devil's advocate part - she may be acting like this because of guilt. I know that no one else has mentioned this, but it is possible that she is acting like this because of something that she has done. I've had to deal with women like this in the past. The guys are all great guys, willing to do anything, give her all the space she needs, and the kids are home with the grandparent's and she is out partying. I had the unfortunate task of letting my homeboy know what was up. She denied it of course, but I had no reason to lie about it.
I am not saying that this is what is going on. What I am saying is - DONT BEAT YOURSELF UP. Sure, be there for her and your kids. Offer to do what you can. Tell her that if she hasn't "found" herself, you don't think she can find it with someone else; but you can't control what she does. Tell her that you don't want anyone else, and that you aren't going to do it, what she does is up to her.
Talk to her parents, if possible, to let them know that you are willing to help out in any way, if they feel that they can call on you, it might help everyone. My only concern is the children, the parents have a tendency to forget that even babies can pick up on tension, and it can affect their health.
Don't want to make anyone mad, just wanted to put my two cents in. Amazingly it mirrors the situation with my son and grandson. My son's girlfriend is a real piece of work.