Is it permissible to abandon a vow that necessitates praying two rak'ahs after each prayer (and four after Maghrib) if being remiss in fulfilling it leads to abandoning the obligatory prayers?

That vowed prayer has become obligatory upon you, like a fard (obligatory prayer). It is not permissible to abandon it; rather, you must preserve it like the fard prayers, because the Prophet, peace and blessings be upon him, said: "Whoever vows to obey Allah, let him obey Him." Laziness is not an excuse to abandon the vow as long as you are capable of fulfilling it.