Is it permissible for one who participates with half a cow in the Uḍḥiyah (sacrifice) to combine the intention of Uḍḥiyah and ʿAqiqah for his two children in it, or is it only for Uḍḥiyah, and he is then required to perform ʿAqiqah for each child with two rams at a later time?

Slaughtering a cow or a she-camel with the intention that part of it be for 'Aqiqah (definition) and the other part for Udhiyah (definition) is a matter of dispute among scholars. The Shafi'is and Hanafis permitted it, while the Malikis and Hanbalis prohibited it due to the lack of evidence supporting it. It is hoped that there is latitude in this matter, but it is preferable to slaughter a separate animal for the 'Aqiqah and another for the Udhiyah to avoid disagreement.