Hi alapete,
It is good that you have concerns about the birth control she wants to use, but this is really a conversation you need to have with her. Is there a reason why she wants to use this method over another?
My wife and I used NFP both to avoid pregnancy and to plan our first pregnancy (due in a few weeks). I know it doesn’t work for everyone - something I don’t think all parish priests are sensitive to when they take a hard line on it. Women with irregular periods or certain medical conditions cannot use it easily if at all, although they’ve apparantly been able to do quite a bit at the Paul the VI Center as far as education and assistance. The downside of NFP is that it calls for brief periods of abstinence (a week at worst), which could be a time of prayer as well as a time to try non-sexual approaches to intimacy - ie, date nights whose sole intent is to shut out the outside world and build your friendship with your wife, etc.
Your wife may not give a flying rat’s bum what the Pope or the Church says, and so wouldn’t care about the prohibition on condoms. She should at least know that it is a concern for you, something that bothers you, and you should have a good discussion on it in the framework of a talk about children, your plans for each other, as well as health and financial concerns. This isn’t an easy issue, but rather is a very delicate one because it goes the core of our identity as people.
As for yourself, if there is another choice then using a condom is always a sin. But if the choice is between using a condom and total abstinence, or worse a deterioration of your relationship with your wife, I think it would be a venal sin at worst. You should still work on it, though - neglecting to have such a talk may lead to more serious problem because it will remain a source of disconnect for the both of you.