Is praying two Rak'ahs with the wife on the wedding night authentically reported from the Prophet, peace and blessings be upon him, and is the husband's prayer alone sufficient if the wife declines?

It is recommended for the couple to pray two rak'ahs upon entering and supplicate for goodness and blessings. Al-Albani graded as good the hadith mentioned in "Adab Az-Zifaf" (The Etiquette of Wedding). It is preferable that they pray in congregation and the wife says 'Ameen' to her husband's supplication. If she does not, the husband has still performed the recommended act, and there is no obligation upon the wife, as the prayer is not obligatory.