Is it considered disobedience for children to use rugs in their private rooms, despite their mother's refusal and her belief that they bring bad luck?

The use of carpets and furnishings is permissible, except for silk, which is forbidden for men. The mother must be certain that all matters are in Allah's hands, and that benefit and harm come from Him, as Allah Almighty says: "Indeed, We have created all things with a [divine] decree." (Quran 54:49). Abandoning carpets due to a belief in their harm might be considered a forbidden form of ill omen (tashā'um) in Islamic law. A Muslim should protect themselves with remembrances (adhkār) and lawful protective measures. You must not use them if your mother is not pleased with that, for fear of psychologically harming her, as harming her is strictly forbidden.