One udhiyah is sufficient on behalf of both spouses and the members of their household

Praise
be to Allah.

Firstly: 

It is permissible for the one who is
offering the udhiyah to share the reward of his sacrifice with whomever he
wants of his relatives, both living and dead, because of the hadith that was
narrated by Muslim, in which it says: “O Allah, accept on behalf of Muhammad
and the family of Muhammad”, and the family of Muhammad includes both living
and dead. It is also permissible for him to offer an udhiyah on behalf of
the dead separately, or along with those who are living. This has been
discussed previously in the answer to questions no.
36596 and 36706.

Secondly: 

One udhiyah is sufficient on behalf of a
man and the members of his household, including his wife, children and
parents, if they all live in one house, because of the report narrated by
Muslim (3637) from ‘Aa’ishah (may Allah be pleased with her), that the
Messenger of Allah (blessings and peace of Allah be upon him) ordered that a
ram with black legs, black belly and black (circles) round the eyes should
be brought to him, so that he could sacrifice it. He said to her: “O
‘Aa’ishah, give me the knife,” then he said: “Sharpen it on a stone.” She
did that, then he took it, and he took the ram and lay it down on the
ground, then he slaughtered it and said: “In the name of Allah; O Allah,
accept (this sacrifice) on behalf of Muhammad and the family of Muhammad and
the ummah of Muhammad.” Then he sacrificed it. 

An-Nawawi (may Allah have mercy on him)
said: This report was quoted as evidence by those who regarded it as
permissible for a man to offer the udhiyah on his own behalf and on behalf
of the members of his household, and to give them a share with him in the
reward. This is our view and the view of the majority.

End quote from Sharh Muslim by an-Nawawi 

Based on that, what is prescribed for the
husband is to intend that his udhiyah is to be on his own behalf and on
behalf of the members of his household, as the Prophet (blessings and peace
of Allah be upon him) said, and that will be acceptable and sufficient on
his own behalf and theirs, and they will have a share with him in the
reward. There is no need to offer a separate udhiyah on behalf of his wife. 

If he did not intend that his udhiyah
should also be on behalf of his family, then they are not required to offer
udhiyah themselves, because the udhiyah is waived from the members of the
household if the man offers an udhiyah, even though they will not be
rewarded for something that they did not do and for which the one who did it
did not give them a share in the reward. 

Ar-Ramli (may Allah have mercy on him)
said, concerning the udhiyah: It is a confirmed communal Sunnah, even if it
is in Mina, if the members of the household are numerous, otherwise it is an
individual Sunnah. What is meant by it being a communal Sunnah, even though
it is Sunnah for each of them, is that it is waived if someone else does it,
although the reward is not attained by the one who does not do it, as is
also the case with the funeral prayer. The author said in Sharh Muslim
that if he gives a share of the reward to someone else, that is valid, and
that is also our view. The basic principle for that is the fact that he
(blessings and peace of Allah be upon him) sacrificed cows in Mina on behalf
of his wives. Narrated by al-Bukhaari and Muslim.

End quote from Nihaayat al-Muhtaaj
(8/132) 

But if the wife has her own money, and she
wants to offer an udhiyah at her own expense, then she may do so. If one of
her sons gives her money with which to offer the sacrifice, and she accepts
that from him, that is also valid. 

For more information, please see the
answer to question no. 45544. 

And that Allah knows best.