What can a veiled girl do who fears her hijab will be uncovered against her will, while her brothers leave her at home with their friends and her cousin?

There is no objection to a woman being in seclusion with non-mahram men if she is safe from temptation, but caution and prudence are necessary. As for the cousin living there, if he is an adult, it is stipulated that Islamic regulations be observed, such as not sharing a common passage and having multiple spacious rooms so that private parts are not exposed. Otherwise, cohabitation is forbidden.