Is Zakat obligatory on money sent to my wife to prepare her for travel and joining me, knowing that the money is still with her, and she has not yet been able to obtain the visa, and it is not designated for trade?

If the wealth reaches the nisaab (the equivalent of 85 grams of gold) and a full year passes over it, zakat becomes obligatory on it. It is not considered that it did not grow in trade or the like, because it grows potentially.