Praise be to Allah.
The udhiyah is an act of worship that is encouraged in Islamic teaching, with no differentiation between men and women, or between married or unmarried women. This is indicated by the general meaning of the texts which speak of the udhiyah, without any restrictions or limitations.
If a woman can afford it, it is Sunnah for her to offer an udhiyah on behalf of herself and on behalf of her household, from her own wealth, especially if the head of the household refuses to perform this ritual.
Ibn Hazm (may Allah have mercy on him) said in al-Muhalla (6/37): The udhiyah for a traveller is the same as it is for one who is not travelling, and there is no differentiation; the same applies in the case of a woman, because Allah, may He be exalted, says (interpretation of the meaning): “and do good” [al-Hajj 22:77], and offering the udhiyah is a good deed. All of those whom we have mentioned need to do good deeds, and are encouraged to do so. If we remember what the Messenger of Allah (blessings and peace of Allah be upon him) said concerning the udhiyah, without differentiating between Bedouin and town dweller, traveller and non-traveller, male and female, we will see that limiting it to any such category is invalid and is not permissible. End quote.
It says in al-Mawsoo‘ah al-Fiqhiyyah (5/81):
Being male is not one of the conditions of it being obligatory or Sunnah. Just as it is obligatory for males, it is also obligatory for females, because the evidence for it being obligatory or Sunnah applies to all. End quote.
Based on that, if the head of the household refuses to perform this ritual, then the wife may undertake it herself, or through another person whom she appoints to buy it and slaughter it on her behalf, whether that is with or without the knowledge of her husband, and with or without his permission, because the udhiyah is a Sunnah for everyone, so if the head of the household refuses to perform it, then his wife may undertake it.
The Prophet (blessings and peace of Allah be upon him) said: “O people, verily the people of every household must offer an udhiyah every year…” Narrated by Ahmad (17216) and Abu Dawood (2788); classed as saheeh by al-Albaani in Saheeh Abi Dawood.
Al-Khateeb ash-Sharbeeni (may Allah have mercy on him) narrated from the author of al-‘Uddah that he said: It is a communal obligation if there are several members of the household; if one of the members of the household does it, that suffices on behalf of all of them, otherwise it is an individual Sunnah.
End quote from Mughni al-Muhtaaj (6/123)
And Allah knows best.