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, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
If the case is as you have stated that that man is the paternal uncle of your daughter, then marrying her is a grave sin and it is invalid. That is because it is a form of incest and requires Hadd (i.e. corporal punishment) according to the opinion of the majority of scholars for the one who did it while he knows well its prohibition, and the child cannot be attributed to him in that case unlike if he did it ignorantly, i.e. he will not be subjected to Hadd and the child will be attributed to him. For details, kindly refer to Fatwa 87416.
Accordingly, it is not permissible for him to have sexual intercourse with her; rather, they must be separated; her guardian must be firm with her and not let him approach her. The DNA testing is not taken into account, for DNA testing is not relied upon in denying the confirmed lineage as stated in a decision made by the Islamic Fiqh Council concerning this, which reads: "It is not permissible to use DNA analysis to confirm the paternity of children whose lineage has already been legally confirmed. The concerned authorities are to prevent this, and impose deterring sanctions in this regard in order to protect people's reputations and to safeguard their lineage." For more benefit, please refer to Fataawa 122944 and 90098.
If the laws in your country do not grant you the right to separate between them, you should try to bring her to a Muslim country to raise the case to a Sharee‘ah-based court.
Thus, if this marriage is invalid in principle and according to the consensus of scholars, there is no point to discuss the fact that your daughter appointed a friend as her Wali or the like. If she turns to Allaah The Almighty in sincere repentance, then Allaah The Almighty will accept her repentance as He The Exalted has promised saying (what means): {But indeed, I am the Perpetual Forgiver of whoever repents and believes and does righteousness and then continues in guidance.} [Quran 20:82]
Also, Abu Hurayrah narrated that the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, said: "Whoever repents before the sun rises from the west, Allaah will accept his repentance." [Muslim]
For more benefit on the conditions of repentance, please refer to Fatwa 86527.
In case she repents, she should be treated kindly and not be blamed for what she had done in the past. Also, she has to please her parents for she made them angry because of her actions. But if she insists on having a relationship with her paternal uncle and it is not possible to separate them, then she and her uncle should be deserted if it is expected that deserting them will be beneficial for them. Indeed, deserting the sinner is permissible if there is a benefit to be fulfilled by that as scholars explained. For more benefit, please refer to Fatwa 18611.
As for the uncle's wife, if her husband insists on having a relationship with his niece, then we advise her to seek divorce from him and not remain with him in marriage for there is no good for her in living with a man who commits incest.
Finally, we should note that whoever committed a sin has to, along with repenting from it, conceal his sin and not tell anyone in order not to remove the screen of Allaah The Almighty for the Prophet, sallallaahu ‘alayhi wa sallam, said: "Whoever has committed any of such filth should conceal himself with the concealment of Allaah." [Al-Bayhaqi and Maalik in Al-Muwatta']
Allaah Knows best.