Is the husband obligated to buy an Udhiyah for his wife if he works abroad and has asked her to spend Eid with her family, while he has bought an Udhiyah for his own family?

The Udhiyah (sacrifice) is a confirmed Sunnah according to the majority of scholars for those who are able to afford it, and it is not obligatory. A husband's contribution to buying a sacrificial animal for his family or his wife is a good deed for which he will be rewarded. It is not obligatory, but it is among noble manners and strengthens the bond between them, in addition to being an act of obedience.