Is it better for a Muslim woman to perform Tarawih prayer in the mosque with her brother so that he also prays, or to remain at home to perform Tahajjud prayer in the middle of the night after Witr prayer? Which one yields more reward?

Combining Tarawih prayer with the congregation and Tahajjud prayer late at night is possible in two ways:

1. Praying Witr with the Imam, then performing Tahajjud in sets of two rak'ahs without repeating Witr, because there cannot be two Witrs in one night. 2. Delaying Witr until late at night. This is done by the worshiper adding one rak'ah after the Imam's salam to make his Witr odd-numbered, so he can pray his Witr after his Tahajjud late at night. This does not preclude him from being considered as having prayed with the Imam until the Imam departs, a practice affirmed and permitted by scholars.