Being pregnant is no easy ordeal, double so with twins. And same goes for the first year or 2 after birth. So her working will put much strain on her and may cause complications during pregnancy, and as the saying goes when the wife is overly stressed so will be the family.
However lets assume she finds a part-time (lets say ~15hrs/wk) stay-home job (as a telemarketer or something) and stress is a non-issue. That job will require much attention from her that will be taken away from the babies. (Multi-tasking is not a viable option here, even if the work is easy, contrary to popular belief you cannot continuously bounce your attention back and forth and not have your performance suffer in its quality.) Unless youre fine with neglecting your babies, you will require a babysitter to watch them while wifey works and youre at school/studying for most of the day. Unless you find a cheap one, a notable chunk of the money wifey rakes in will go to the sitter's pocket and also dont forget sitter's charge extra for each baby they watch and youll have 2. At the end of the day her net income will be unsatisfactory to the both of you.
I think it would work out better for your family if you and your wife were able to get monetary help from each of your own parents. If thats not an option, maybe take out a bigger loan. If neither of those 2 are an option, then I have to ask the very obvious question and I dont mean any offense by this but: why did you decide to have kids if you couldnt afford it?
Personally I see myself being in a very similar situation as you but when I am halfway through D school instead: with a pregnant (stay-at-home) wife and living far from parents, like you. But I know my parents will financially support us and if thats not enough future-wifey's parents would help as well if theyre able. If no other solution springs to my head then my last resort would be taking out a larger loan.
Anyways, BIG congratulations on the twins and on wisely setting up your marriage as a single-income family, you and your wife will be spared all the silly drama and marital instability a 2-income household would normally experience.