All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
Scholars of Fiqh agree that it is obligatory to be fair to the wives in terms of overnight stay, financial maintenance and clothing. They differ on the extra matters concerned with financial maintenance such as gifts:
The first opinion sees permissibility of inequality. Ibn Qudaamah said, “He does not have to treat his wives equally in financial maintenance and clothing if he does what is required of him for each of them. Ahmad said, ‘Concerning the man who has two wives – he has the right to favor one over the other with regard to financial maintenance, desire and housing, if the other has enough, and he may buy a finer garment for her, so long as the other has enough.’”
The second opinion sees the obligation of equality in any case. There is no doubt that this approach is more pious. This opinion brings as evidence the Hadeeth narrated by Abu Hurayrah where he said that the Prophet, sallallaahu ‘alayhi wa sallam, said: “Whoever has two wives and he is more inclined to one of them than the other, he will come on the Day of Judgment with one of his sides sliding down.” [Abu Daawood, At-Tirmithi, Ibn Maajah and An-Nasaa’i]
Shaykhul-Islam Ibn Taymiyyah said, “There was a difference among scholars regarding fairness in financial maintenance (to the wives) whether it is obligatory or recommended. However, being obligatory is a sounder opinion and more conforming to the Quran and the Sunnah.”
On the basis of the opinion which permits inequality in matters beyond obligations, it is permissible for you to give that wife alone such a gift. If you give the other wife a similar amount of money in case of any occasion she has, this will be safer and nearer to fairness.
Allaah Knows best.