Is it better for a capable son to donate the price of the sacrificial animal to his poor father so that the father may offer the sacrifice, or for the son himself to offer the sacrifice?

The Udhiyah (sacrificial offering) is a confirmed Sunnah for whoever can afford its price in excess of their needs and the needs of those they support. If the members of a household share the same dwelling and expenses, one Udhiyah suffices for them, and it is valid for all household members, including the parents. The father can be given the price of the Udhiyah to perform it on behalf of the entire household, or it can be gifted to him so he may sacrifice it. However, it is preferable for the sacrificer to be the owner of the wealth if he is independent. As for a son who is independent in his own home, he does not sacrifice on behalf of his parents residing in another house unless he gifts them the price of the Udhiyah.