Do I recite dua qunoot loudly or silently while praying witr in congregration with my wife? If loudly, What is she supposed to say or do while I'm reciting dua qunoot?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

The Qunoot supplication in Witr is a matter of difference of opinion among scholars, and based on the opinion that regards it as mustahabb (recommended or encouraged) such as that of Hanbalis, then you recite the Qunoot supplication aloud, and your wife says “Ameen” to your supplication. The Hanbali school of jurisprudence stated that the imam should recite the supplication out loud and the Ma'mum (a person who is led prayer) should say “Ameen”.

Sharh Al-Muntahaa, which is a book on Hanbali Fiqh, reads, “it is recommended for the praying person to make Qunoot in the last rak'ah of Witr prayer after standing up from bowing, to raise his hands in Qunoot up to the level of his chest, while turning his palms towards the sky, even if he was Ma'mum (led in prayer) and to say out loud the (supplication) and the Ma'mum responds by saying “Ameen” to the Qunoot of the imam if he hears it.”

Allah knows best.