A woman took a vow to slaughter an animal sacrifice as ‘Aqeeqah (i.e. the sacrifice done for a newborn) when she gave birth to her daughter, but she could not do so then. She gave birth to a son, and when he got sick, the woman vowed to slaughter another animal sacrifice if he recovered from his illness. Can she offer a single sacrificial animal as ‘Aqeeqah for the two children?
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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 is His Slave and Messenger.

It is disliked to take vows that are conditional on the occurrence of a particular thing, such as a patient's recovery or having a child, according to most of the scholars. However, the vow-taker is obliged to deliver on such a vow once the condition is fulfilled (i.e. the thing upon which he conditioned his vow takes place). Allaah, the Exalted, says (what means): {(Then let them…) and fulfill their vows...} [Quran 22:29] Moreover, the Prophet, sallallaahu ‘alayhi wa sallam, said: "Whoever vowed to offer an act of obedience to Allaah, the Exalted, must do so..." [Al-Bukhari]

Therefore, this woman should fulfill her first vow, which was conditioned on her daughter's birth. She is also required to fulfill the second vow, which was conditional on her son's recovery from his illness. Both vows should be fulfilled, and it is not sufficient for her to offer one animal for them both. This is because they are two separate vows with different times and reasons.

Her inability to fulfill her first or second vow does not cancel the obligation of fulfilling them whenever she can. So, she has to fulfill those vows whenever she becomes able to fulfill them. She is not exempted from the obligation of fulfilling these two vows unless she is entirely unable to fulfill them. In case of inability to fulfill her vows, she should offer an expiation like that for breaking an oath. Ibn ‘Abbaas reported that the Prophet, sallallaahu ‘alayhi wa sallam, said: "Whoever makes a vow and does not specifically state it, the expiation (for such a vow) is the expiation for breaking an oath. Whoever makes a vow and is not able to fulfill it, the expiation for that is the expiation for breaking an oath..." [Abu Daawood and Ibn Maajah]

Allaah Knows best.