You are missing the point of having to switch back and forth between the two twins.
To answer your question: imagine that they need to perform the teleportation trick. One of them disappears, and the other one shows up somewhere else at the same time. The other must look exactly like the one who disappeared, wearing the same outfit, having the same props and (naturally) the same wounds/scars/ etc.
If the audience suspect for a tiny bit that the guy who appeared in a different location has a slight difference than the other one (who just disappeared), they will be on the trick and the effect will wear off quickly.
That is why they need to make sure they stay "synced and updated" to each other if they are to perform the trick at any given moment. Keep in mind that the trick has to work in reverse as well, so each of the twins must know how to talk, act, and behave as the other to avoid raising any suspicion.
Knowing all of the above, we come to your question: why involve the wife with the twin (after duplicating the injury to his hand)?
The way I see it, it is nearly impossible to hide an injury from your spouse, so she has to know about it sooner or later. That's fine, we are only talking about one of the twins so far (the one who fell in love with the girl and got married to her).
Now, what we have so far, is the husband with an injured hand and an engineer with a good hand.
At this state, they can not perform the trick because one of them is different that the other (not only by looks, but also by the way an injured man moves and uses his hand).
so they must be "synced". So they do it and they duplicate the injury on the engineer's hand. Now they are equal, but wound on the engineer is fresh and needs dressing, taking care. They help each other first, but they are equal, which means, they can perform the trick again.
Well, guess what: they do the trick and the "husband" disappears while the "engineer" appears somewhere else and people think he teleported. The husband must stay hidden to fool everyone, including his wife, and the engineer must take his place and goes home to fill in his space. The wife notices the wound is fresh, and possibly notices other "things" while her real husband is in the engineer disguise.
To make it short, they had to switch places because it would be difficult to keep the secret from the wife and still perform the trick in public (which includes the wife).
That is my point of view. For all I know, they could have done all of that so that we as audience can later fill in the blanks and to make it more interesting, but I agree with you, it was a stupid decision to make.
EDIT: I forgot to mention that it's been almost 8 years since I saw the movie. So when I refer in my answer to (the wife) I mean (Scarlet Johansen). I forgot if there were another love involved in the life of the twins.