carpe diem

Agreed. Even family members and very close friends never know the whole story of a couple's relationship. I have seen friends stay with someone who did horrible things to them and as an outsider have been absolutely dumbfounded. Similarly I have seen people walk out of a relationship that seemed to be working very well. I have decided not to judge friends for their relationship decisions and just to try to help them and to get along with their significant others no matter how I think of them. So, this is a long introduction to say, go with what you feel, not with how others analyze the situation.
You will probably never know what your husband's motivations were throughout the dating process and when entering into marriage. Moreover, most people (not just immigrants) are moved by a variety of considerations in these matters-- in addition to love, friendship, and perceived long-term compatibility, many are motivated by things like financial security, fear of staying alone, wish to start a family, social pressure, convenience, and yes, immigration status or the possibility to move to a more desirable country. Most individuals are complex and so are most relationships.
Of course, there are scammers who do anything, everything just to get a GC over the back of an unsuspecting USC. But from reading your account, this doesn't seem to be the case in your relationship. I would say, as hard as it is, try to focus on picking up the pieces and taking good care of yourself, not on making his life more difficult.
Best of luck! You will be very happy again one day.

I'm going to add something that may sound kind of heartless. I know you love your children and I'm sure they're wonderful. But as a highly-educated career woman who doesn't particularly relish spending a lot of time with other people's children (as an aside I'm undecided about whether I want to have children of my own although I think -- and many other women who have been in the same situation have confirmed this -- things might be different when they're yours), I would positively go crazy if I moved all the way across the world, only to find that my husband drags his feet getting my work papers in order and expects me to use my first few months here to warm up to his children and take care of them, however little he seems to be asking from his perspective. I'm not saying she shouldn't try to build up a relationship with your children. I'm saying they are YOUR children, not HERS (and her problems with getting pregnant probably make this all the more painful to her) and things might have worked better had she been able to build a relationship with them from a place where she is out of the house most of the day just like you are, having her own things, doing work where she can put her education and intelligence to use or at least where there is some chance of being able to do that down the road, learning about working in the US, and contributing financially. Of course she is exaggerating when she refers to herself as being a "slave" but I can relate somewhat to that feeling as she is basically being pushed in the role of the one who takes care of the children and the home and to her this probably feels like violence to her personality. And you working exceptionally long days makes this role patron worse-- if you're working these kinds of hours YOU haven't been contributing enough to your home and family life.
Your children and your mom are strangers to your wife, from a different culture-- and your mom probably thinks your wife landed the best deal ever with you (because that's how all moms feel about their sons) and I'm sure feels protective of her grandchildren who have gone through a rough time. I don't know how old your children are but in my experience young children perfectly understand it when you're not their parent and it's very difficult for a non-parent to set limits-- and probably more so when you're "daddy's new wife" who needs to build a lasting relationship with the children than when you're a nanny who has a more professional relationship with the family. In sum, the people with whom she spent most of her time were probably the least capable of understanding your wife's adjustment problems. It sounds to me like she was extremely isolated, only spent time with the people who are the closest to you and therefore probably not entirely receptive to her problems, and instead of being able to find her own way in this country by working, meeting other people through her professional life, maybe engaging in a community activity that's something she really loves doing and that allows her to build a bit of a life separate of yours, she was expected to make it a priority to build a relationship with your children and to cook for your church.
You sound like a great guy and you clearly love your wife, but I think you may have underestimated how hard this adjustment has been and how offensive it may have been to her that you didn't make it your first priority to help her get started in this country by applying for EAD and AP right away (especially seeing how you managed to "find" the sums for private school and other emergencies). Yes it's a lot of money but it sounds like you could have made it work if you really wanted to, and once she starts working it's earned back in no time.
I very much hope she will come back to you. If she does, please do everything you can to give her a good "re-start"-- at least help her find work, start looking into another solution for your mom, and do not make it your wife's primary responsibility to take care of your children (you managed before she moved to the US!). Also, and I think this is very important: Try to find someone she can talk to, either a psychologist or a social worker or a religious person, but it has to be someone who has NO ties to you. You're American and probably very sociable (and had your work connections to get you started); even though your town is new to you too, it is clear that you've been able to make connections and build a life for yourself in a pretty short time. It is important for her to be able to talk to someone who is not connected to you, who will not report back to you, to whom she can say how she really feels about her situation, the kids, your family, without fearing that what she says will reach you. As you recognize, sometimes we all need to vent and say things that we don't necessarily mean but just want to get off our chests and it's essential for her to be able to do that without being afraid to complicate her relationship with you and your family.
Best of luck. I hope we'll get to see a happy update one day.