Is it permissible to perform a two-rak'ah prayer lightly, then recite Surat Al-Baqarah, or to perform the prayer with the entire Surat Al-Baqarah over several days, in fulfillment of a vow to pray two rak'ahs on the wedding night with the entire Surat Al-Baqarah, considering that the two rak'ahs of the wedding sunnah are light and there is hardship in praying with the entire surah in one night?

Undertaking a vow (nadhr) is disliked (makrooh), and it is obligatory to fulfill it in the manner you specified. Praying two light rak'ahs or gradually praying with Surat Al-Baqarah will not suffice. The difficulty here does not permit breaking the vow or changing it. Your wife is not obligated to share in fulfilling the vow with you, but it is better for her to assist you, based on the Prophet's (peace be upon him) saying: "A son of Adam is not bound by a vow concerning what he does not possess," and because that is part of cooperating in righteousness and piety.