Praise be to Allah.
The marriage contract mentioned is valid and your father can be counted as a witness to your marriage. This is the view of Imam al-Shaafa’i and was narrated in one of the reports from Imam Ahmad (may Allaah have mercy on them both).
See Nihaayat al-Muhtaaj, 6/218; al-Insaaf, 8/105
That is because he is not a wali (guardian) with regard to marriage, so he may be a witness, unlike the wife’s father.
The view that this is valid was favoured by Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him). After mentioning the first view on this matter, which is that it is not permissible for any ascendant (father, grandfather, etc) or descendant (son, grandson, etc) of either spouse to be a witness to the marriage, he said: The second view is that this is valid, and one or both witnesses may be an ascendant or descendent.
Then he said: So the correct view is that the marriage contract is valid. This was narrated from Ahmad and was the view favoured by many of our companions.
Al-Sharh al-Mumti’, 5/163
Moreover you mention that you have been married for two years, so it may be assumed that the marriage has been announced publicly, such as inviting people to a wedding party and so on, as is customary among people nowadays. This is sufficient to make the marriage valid, even if it was not witnessed by two witnesses, according to some scholars. This is the view favoured by Shaykh al-Islam Ibn Taymiyah who said: There is no doubt that a marriage that is announced publicly is valid, even if it is not witnessed by two witnesses.
Al-Ikhtiyaaraat, p. 210
The wife’s father erred by saying that he had received the dowry when in fact he had only received half of it, but that does not affect the validity of the marriage contract.
And Allaah knows best.