Is my prayer and my brother's prayer complete, knowing that I said the Taslim twice in the third and fourth rak'ahs and performed the prostration of forgetfulness (sujud al-sahw), and my brother intended to pray Maghrib then completed the last rak'ah with me?

The Imam is not permitted to rely on the tasbeeh of a single congregant, because the Imam relies only on the tasbeeh of two just witnesses. The people of knowledge have stipulated this, among them Ibn Qudamah in Al-Mughni, Ibn Rushd in Al-Taj wal-Ikleel, Al-Dardir in Al-Sharh Al-Kabeer, and Fath Al-Wahhab for the Shafi'is. Therefore, you must repeat the prayer, and your brother is also required to repeat the prayer.