Obviously, the Tang family, especially the Zhang family, vehemently went against Tang Lixue's wish to take in his daughter as part of the family. The Yan family had no interest in raising his daughter and Tang Lixue couldn't just abandon his daughter while he sought revenge on those who harmed his family.
His estranged wife had taken in a girl and let her bear the Tang surname, then why the hell wouldn't they let his little Moyu join the family? Eventually, they had no other choice but to allow Tang Moyu to live with them temporarily.
He and Zhang Wuying were trapped in a deadlock for years, and hadn't seen eye to eye with each other. He knew that she despised his daughter and couldn't accept the fact that she'd been forced to accept his daughter from another woman to save face. Zhang Wuying, a prideful woman like her, would never allow her reputation to be tarnished by Tang Moyu's existence.