Unfortunately, the answer to your tax question is no. Sending money to family or friends overseas (even when or if they really need it) is not considered a charitable contribution, for purposes of qualifying as a tax deduction. Gift taxes are something different entirely, but you don't get a tax deduction for making gifts either.
Basically, the IRS and the federal tax laws tell us that individuals cannot be the recipients of charitable contributions, that can reduce someone's taxes in the form of taking a deduction. Only charitable groups and certain non-profit institutions can be such tax-deductible recipients of charity. Perhaps an example will be helpful.
Let's take a hypothetical sick or injured person seeking treatment in a not-for-profit hospital. You could not take a charitable tax deduction for giving money directly to this person for their support or medical care; but you could take a tax deduction for giving money to the hospital itself, as that would benefit a whole class of people, and not just one person or family. Does that reasoning make sense?
Additionally, there are significant restrictions on (tax deductible) charitable donations for institutions located outside of the United States (in other words, foreign). So that's an additional restriction we would have to consider.
All that said, however, doesn't mean that sending money to help your wife's family isn't a good thing to do; it just means that you cannot (legally) take a charitable tax deduction for doing so.
Thanks for asking this important question.
