What is the ruling regarding a girl removing her hijab in Western countries with her parents' consent, and what is the role of the brother towards his parents and his sister who refuses the hijab, considering it a minor matter?

It is forbidden for a woman to remove her hijab in front of non-mahram men, whether in Western countries or her own country. Her guardian must command her to wear the hijab and compel her to do so, because true well-being lies in obedience to Allah and His Messenger (peace be upon him). Furthermore, there is a concern that a father who condones his daughter removing her hijab might fall under the meaning of "dayyuth" (a cuckold/pimp) as mentioned in the hadith.