Is it permissible to go to the mosque for Tarawih prayers, leaving the mother alone at home, or is it better to pray them at home to obtain the same reward?

It is permissible for a woman to perform Tarawih prayers in congregation at the mosque, provided certain conditions are met. However, her prayer in her home is better and carries greater reward. If her going to the mosque would cause harm to her mother due to her being left alone, then she is obligated to stay with her to avert this harm, based on the Prophet's (peace be upon him) saying: "There should be no harm nor reciprocating harm." Staying with someone who is feared to be neglected is considered one of the justifications for missing Jumu'ah and congregational prayers.