Assalam O Alaikum WaRahmatullahi WaBarakatuhu brother Imran,
You can look into the thread below for more details, especially towards the end of my very first post which has more details and fiq related Q/A related to Udhiya ( Qurbani):
Month of Dhul Hijja - Some hadiths, virtues, rulings for Udhiya
if you don’t have time, the the simple answer is that you can sacrifice one animal on behalf of your entire family. The evidence is Hadith below:
It was narrated from ‘Aishah and Abu Hurairah that when the Messenger of Allah (ﷺ) wanted to offer a sacrifice, he brought two large, fat, horned, black-and-white, castrated rams. He slaughtered one on behalf of his nation, for whoever testified to Allah with monotheism and that he had conveyed (the Message), and he slaughtered the other on behalf of Muhammad and the family of Muhammad (ﷺ).
حَدَّثَنَا مُحَمَّدُ بْنُ يَحْيَى، حَدَّثَنَا عَبْدُ الرَّزَّاقِ، أَنْبَأَنَا سُفْيَانُ الثَّوْرِيُّ، عَنْ عَبْدِ اللَّهِ بْنِ مُحَمَّدِ بْنِ عَقِيلٍ، عَنْ أَبِي سَلَمَةَ، عَنْ عَائِشَةَ، وَعَنْ أَبِي هُرَيْرَةَ، أَنَّ رَسُولَ اللَّهِ ـ صلى الله عليه وسلم ـ كَانَ إِذَا أَرَادَ أَنْ يُضَحِّيَ اشْتَرَى كَبْشَيْنِ عَظِيمَيْنِ سَمِينَيْنِ أَقْرَنَيْنِ أَمْلَحَيْنِ مَوْجُوءَيْنِ فَذَبَحَ أَحَدَهُمَا عَنْ أُمَّتِهِ لِمَنْ شَهِدَ لِلَّهِ بِالتَّوْحِيدِ وَشَهِدَ لَهُ بِالْبَلاَغِ وَذَبَحَ الآخَرَ عَنْ مُحَمَّدٍ وَعَنْ آلِ مُحَمَّدٍ ـ صلى الله عليه وسلم ـ .
Grade : Hasan (Darussalam)
English reference : Vol. 4, Book 26, Hadith 3122
Arabic reference : Book 26, Hadith 3241
https://sunnah.com/urn/1272250
and Q/A in the video below:
I also want to point out that Hanafi madhab has a different view. They consider udhiya has Wajib on every adult who has minimum Nisab to pay Zakat. However, other madhabs don’t consider Udhiya as Wajib. They consider it as Sunnah Mu’akada which means one should try to give Udhiya if they are able to and if they don’t then there is no sin but they may miss on huge reward.
And Allah knows the best!
Ma’aSalaam