Praise be to Allah.
This vow comes under the heading of vows to do acts of worship and obedience, so it must be fulfilled, whether it was general or conditional. A general vow is when a person says, for example, “I vow – or I promise to Allaah – that I will sacrifice a sheep, or give it to the poor or to my relatives.”
A conditional vow is one where a person says, for example, “If Allaah heals me, or if I succeed, or I get a salary, or I acquire such and such an amount of money, I will offer a sacrifice etc.”
With regard to the obligation of fulfilling the vow, that is because the Prophet (peace and blessings of Allaah be upon him) said: “Whoever vows to obey Allaah, let him obey Him, but whoever vows to disobey Allaah, let him not disobey Him.” Narrated by al-Bukhaari (6318).
So long as you did not stipulate a specific time for fulfilling your vow, then it is permissible for you to fulfil it at any time, during the days of Eid al-Adha or at any other time.
But if you intended to offer a sacrifice this year, the sacrifice in fulfilment of your vow does not count as the udhiyah sacrifice too, even if it is sacrificed during the days of Eid al-Adha.
If a person vows to offer a sacrifice and give the meat to his family, relatives and the poor, that includes his immediate family such as his wife and children, because they are part of his family, unless he intended to exclude them, in which case it should be done as he intended.
As for the one who made the vow, he is not entitled to eat from the sacrifice he vowed to offer. If he does eat some, he must give the value of that to the poor.
The fuqaha’ (may Allaah have mercy on them) stated that he should not eat any of the meat of the sacrifice that he vowed to offer.
See: Haashiyat Ibn ‘Aabideen (2/616) and al-Mughni (3/288).
One of the reasons that the fuqaha’ gave for the one who made the vow not being allowed to eat any of the meat is that if you vowed to give it to the poor, for example, then it is only for them, and you are not allowed to divert any of it away from them. See al-Muntaqa by al-Baaji (2/318).
In al-Mawsoo’ah al-Fiqhiyyah (6/117) it says: With regard to a vow, it is not permissible for the one who made the vow to eat any of the sacrifice that he vowed to offer, because it is charity and it is not permissible to eat from one's charity. This is in general, because there is a difference of opinion with regard to a sacrifice that one has vowed to offer. Similarly with regard to a general vow that one has not vowed to give specifically to the poor – whether verbally or in one's intention – it is permissible to eat from it according to the Maalikis and some of the Shaafa’is. End quote.
And Allaah knows best.