Your wife is having some huge anxiety over her pregnancy and being alone with the baby, and that needs to be addressed at the core, not in the outward behavior. You can choose to deal with your travel or not, but if you guys don't find out what is going on in her feelings, it's going to keep running from one thing to another.
I suggest that you get to counseling as soon as possible and get this handled before the baby. She may need reassurance, help, support....all kinds of things, but I guarantee you she does not need an out of work husband with a new baby. Jobs are hard to come by right now, and you can't just throw yours away with this economy. Counseling will give you a coach to help you make some compromises that are reasonable and based on the true issues at hand, rather than fears.
Marriage at gunpoint (the threat of taking your child away) never works. You also have some legal rights about having a child taken out of the country. It needs to not come down to that. Get help now.
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