Is the husband obligated to refrain from fasting supererogatory fasts during vacation to avoid disputes with his wife, who believes that fasting affects family time and her marital rights?

Your wife does not have the right to prevent you from observing a voluntary fast on the pretext of sitting together for a meal or because it affects her marital rights. The times for fasting are limited, and her rights can be fulfilled at night. A wife should be a helper to her husband in his obedience to Allah. Nevertheless, one who observes a voluntary fast is his own master, and if a husband occasionally foregoes some voluntary fasting to achieve a legitimate purpose, such as pleasing his wife, it may be a good thing that strengthens their marital relationship.