Is it permissible to marry for a second time to lower one's gaze and apply the Sunnah, if this marriage angers the parents?

Marrying a second wife has the same ruling as marrying a first wife. If it is obligatory, then it is not permissible to obey one's parents if they forbid it, unless their prohibition is specific to marrying a particular woman. However, if the marriage does not reach the level of being obligatory, then it is incumbent to obey them and not disobey them, especially if their prohibition is justified.