In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner, we are greatly pleased to receive your question which shows the confidence you place in us. May Allah reward you abundantly for your interest in knowing the teachings of Islam!
There is nothing wrong that you perform the Tarawih Prayers at home with your family. Also, holding the mushaf (copy of the Qur’an) in your hands is also permissible during the performance of the Tarawih.
Responding to the question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states the following:
There is absolutely nothing wrong for you if you perform Tarawih Prayers at home and read from the Qur’an by holding the mushaf (copy of the Qur’an) in your hands. We have precedents for this in the practice of as-salaf as-salih or the pious forbears; we read in the sources that `A’ishah, the beloved wife of the Prophet (peace and blessings be upon him), told her mawla (client) to lead them (women) in Tarawih; while doing so he was reading from the mushaf (as per her instructions).
Based on this, there is nothing wrong in your case if you were to read from the mushaf while performing Tarawih at home.
If you have any further questions, please don't hesitate to write back!
May Allah guide you to the straight path, and guide you to that which pleases Him, Amen.