I also agree with much of what has been said. But I will draw our attention to the fact that the wife accepted the terms and I suspect was not strong armed into the marriage and coming here. Any responsibility for the current predicament should perhaps at best be shared.
I totally agree with Pete (as usual) that he is the man and should assume the leadership position but surely as the mother with the primary responsibility for the kids she should have weighed up the constraints with their interests in mind. Perhaps she did and that is why she is here.
Anyway, moving forward:
There are certainly Govenment benefits to be had but things will still be hard but as long as all parties are committed to working things out constructively then all should be well. The wife should not be blaming her husband and vice versa.
Good luck to you!