Is it permissible to slaughter a cow with the intention of ʾUḍḥiyah (sacrifice) on the day of Eid al-ʾAḍḥā and feed wedding guests from it, knowing that the guests offer monetary gifts to the couple?

If the conditions for Udhiyah (sacrifice) are met in a cow (two years old and free from defects), then it suffices for both Udhiyah and the wedding feast, as mentioned by Al-Kharashi and others. As for the attendees donating money to the wedding host, this does not harm the Udhiyah unless the money is in exchange for the food; otherwise, the Udhiyah would become for money, and common custom is equivalent to a condition.