What is the ruling on going to a distant mosque to perform the Tarawih prayer, when there is a mosque close to home, due to the short duration of the Tarawih prayer in the nearby mosque, the lack of devotion among women there, and their failure to straighten the rows?

There is no harm in praying in any mosque, and it is permissible to go to a further mosque if there are good reasons for doing so, such as the Imam prolonging the recitation or to avoid the disturbance of children. This increases the reward due to the greater number of steps, as every step to and from the mosque is counted as a reward for the worshipper.