To make the case clear, let's assume that no matter which of your only two options you pick, there will be seriously bad consequences. And let's agree that this makes both choices bad choices. There's nothing odd to the ear about the phrase "My only options are bad ones." But now let's add another assumption: the consequences of robbing the bank, though genuinely bad, would not be nearly as bad as the consequences of letting your children starve. Though I can imagine certain sorts of objections about long-term consequences, set those aside. Surely it's possible for one thing to be less bad than another, even if both things are bad. Killing someone may be bad; killing them in their sleep is less bad (to put it mildly) than torturing them to death over a period of several days.
I'd suggest that we can add another premise—a moral premise: if you have no alternative to doing either X or Y, and if X is clearly worse than Y, you should do Y.
As we've set things up, it seems to follow that you should rob the bank. And if you really were in a situation like this, surely that's what would matter.
But, you ask, is that the correct decision—the right decision?
Well, given the alternative, as your wife says, it's the right decision in the sense of being the thing you should do, all things considered. It's not a thing that good in itself; it's not a thing that you should do if there were a better alternative; it's not something that it would normally be right to do; it doesn't avoid wronging anyone. But as things work out, it's still what you should do. What, exactly, is left to argue about?
Well, harming others who've done nothing to deserve it is a wrong. But the word "wrong" is subtle. Robbing the bank can be a wrong, and yet not be the wrong thing to do given the alternatives. We can say that; it makes sense of the situation. And I suspect that you and your wife agree about it.
We could quibble about exactly how to use the words "wrong" or "incorrect," or "right," for that matter. But quibbling is exactly what that would be. Both choices are bad choices, yet one is less bad than the other, and that's the one you should pick. If that's agreed, then what really matters is settled. There's no deep philosophical fact about precisely which way of using words like "wrong" is really right.