His sacrifice (udhiyah) was slaughtered without him giving any instruction to that effect
Question

I had told my father that I was going to offer my sacrifice on the second day of Eid so as to avoid overcrowding, but on the first day I found my brother knocking on my door, and he had my slaughtered sacrifice with him. He said: Our father instructed us to slaughter it with the other animals. What is the ruling on the sacrifice?
Praise be to Allah.If a Muslim has singled out his sheep to be slaughtered as a sacrifice, and someone else slaughters it without his permission, then the sacrifice is valid, so long as it was slaughtered at the time of sacrifice, and the one who slaughtered it was acting on behalf of its owner.
It says in al-Mawsoo‘ah al-Fiqhiyyah al-Kuwaitiyyah (5/105):
The fuqaha’ are unanimously agreed that it is valid to appoint someone to slaughter a sacrifice on one’s behalf, if that proxy is a Muslim. End quote.
The basic principle with regard to permission to act as a proxy is that permission should be given verbally, but it is also valid on the basis of what is customary.
Ibn al-Qayyim (may Allah have mercy on him) said:
The basic principles of Islamic teaching indicate that permission according to what is customary is the same as permission given verbally. End quote from Madaarij as-Saalikeen (2/1019).
What is customary and the situation at that time indicate that you had given your father permission to act on your behalf with regard to slaughtering the sacrifice, so this sacrifice that was done on your behalf is valid.
Al-Qudoori al-Hanafi (may Allah have mercy on him) said:
Our companions (may Allah have mercy on him) said: If someone else slaughters a person’s sacrifice without him instructing him to do so, that is good enough for the owner of the udhiyah and it is regarded as an udhiyah for him, and the one who slaughtered it is not liable.
Ash-Shaafa‘i (may Allah have mercy on him) said: The sacrifice is valid.
We think that what is most likely to be the case is that the individual does not slaughter his sacrifice himself; rather he appoints someone else to do it on his behalf and usually pays him a fee for that. So the udhiyah must be sacrificed, and the owner of the udhiyah is pleased that there is someone to undertake the slaughtering, so the one who slaughters it has permission to do that according to what is customary, and permission based on what is customary is like permission given verbally. End quote from at-Tajreed (12/6341).
Abu ‘Abdillah al-Khurashi al-Maaliki (may Allah have mercy on him) said:
As appointment of a proxy may be done verbally, it may also be done on the basis of tradition, which takes the place of verbal appointment. But if the slaughterman is a relative of the one who is offering the sacrifice, and he usually takes care of his relative’s affairs, and he slaughters his sacrifice on his behalf, then that is acceptable on behalf of the owner (of the animal), according to the well-known view. End quote from Sharh Mukhtasar Khaleel (3/43).
An-Nawawi ash-Shaafa‘i (may Allah have mercy on him) said:
If a stranger slaughters an animal (udhiyah) that has already been singled out for sacrifice on his own initiative at the time of offering sacrifice, or he slaughters an animal (hadiy) that has already been singled out for sacrifice after it reaches the place of sacrifice, then the well-known view is that the sacrifice is valid.
That is because slaughtering it does not require an intention, so if someone else does the deed, it is still valid, like removing impurity. End quote from Rawdat at-Taalibeen (3/214).
Al-Mirdaawi (may Allah have mercy on him) said:
If a slaughterman slaughters it at the appropriate time without his permission, it is still valid, and the one who slaughtered it is not liable.
If someone other than its owner slaughtered it, either with the intention of doing so on behalf of its owner, or with no specific intention, or with the intention of doing so on his own behalf, if he intended to slaughter it on behalf of its owner, then that is valid on his behalf, and the one who slaughtered it is not liable. This is our view, and it is the view of our companions, and it was stated definitively in al-Furoo‘ and elsewhere. End quote from al-Insaaf (9/387).
And Allah knows best.