Did Tao Xiaodong stay with Tang Suoyan's parents later?

Not together. Tao Xiaodong is the sister of Tang Canaan, the heroine in the book, and had a love affair with Tang Keyan. Tang Keyan's father is a powerful man. He wanted to marry Tao Xiaodong for his own purposes, but he didn't get it in the end. Tao Xiaodong's lover is the mother of another woman Lu Xinyi in the book. In the novel, Lu Xinyi and Tang Suoyan are finally happy together, which shows that Tao Xiaodong and Tang Suoyan's parents are not together.