Is it permissible to hold separate sessions for reciting the Qur’an during trips, with each session supervised by someone proficient in recitation who can correct mistakes?

There is no harm if a person corrects and rectifies the mistakes and shortcomings of a group of reciters gathered to read the Qur’an, provided he is qualified to do so. This is an act of goodness and a righteous deed that benefits them all and helps establish the Qur’an without error.