Is it obligatory to perform Tarawih prayers with a single ablution, or is it permissible to interrupt them, leave the house, and then complete them upon returning, knowing that re-performing ablution might be necessary in this case?

What is established from the righteous predecessors is the continuation of Tarawih prayers without interruption, except for a resting break between every four rak'ahs. Interrupting Tarawih to speak with one's mother is contrary to what has been narrated from the predecessors, even if there is no evidence prohibiting it. It is not a condition for Tarawih to be performed with a single ablution (wudu'). If ablution is nullified, it must be renewed to complete the prayer, because purity is a condition for the validity of prayer, as the Prophet, peace and blessings be upon him, said: "The prayer of one of you is not accepted if he invalidates his ablution until he performs it again."