All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His Slave and Messenger.
If the situation is as you mentioned - that the father denied authorizing your wife's adult son to act on his behalf as her Wali (guardian) in marriage, then by default, he did not authorize him until the opposite is proven, pursuant to the Fiqh principle that reads Al-Asl Al-'Adam, i.e. a fact or rule which had not existed in the past is presumed to be non-existent until its existence is proven.
However, the question involves some issues over which the jurists have differed in opinion:
1- Can a more distantly related Wali marry off a woman instead (or despite the existence) of a closer Wali? Some jurists considered this marriage to be correct and valid while others prohibited it. A third group of jurists said it is acceptable on condition that (the closest) Wali permits it.
2- Who takes precedence in marrying off a woman, the father or the son? According to the Maaliki School, the son takes precedence, contrary to the view of the majority of the scholars. For more benefit on the order of the guardians in marriage, please refer to Fatwa 83338.
Based on the above, it is better to renew the marriage contract in order to be on the safe side, especially since the father is not objecting to this. So we assume that it should be easy.
Allaah Knows best.