Is it permissible to go to the Quran memorization center and endure the brother's punishment for the sake of the Quran, knowing that he prevents his sister from going because she covers her face from her married cousin?

To continue memorizing the Quran and avoid your brother's punishment, try to improve your relationship with him and explain that your commitment to Allah's Sharia necessitates his support, not his hindrance. Endear yourself to him with gifts and kindness, and supplicate to Allah to soften his heart. If he insists on preventing you and you fear his punishment, you can contact a female Quran teacher by phone. If your father is alive, ask him to intervene. And if you can go out without his knowledge, there is no sin upon you if you are safe from harm.