First of all, Duan Yanqing knew that Duan Yu was his son after reading Duan Yu's eight characters, because when he saw Dao Baifeng, he knew that she was the goddess of mercy outside Tianlong Temple.
When he saw Duan Yu's eight characters, he knew that Duan Yu was not Duan Zhengchun's son, but his, so he saved Duan Yu at a critical moment.
Then, Mu Rongfu wanted to kill Mrs. Wang, which should be said to be induced by Duan Zhengchun. Duan Zhengchun looked at the women he liked and indirectly died at Mrs. Wang's hands, and decided to avenge them. Therefore, in front of Mu Rongfu, he said that it didn't matter if Mu Rongfu killed those women, and he only cared about Mrs. Wang. And in order to force Duan Zhengchun to step aside, Mu Rongfu naturally threatened to kill Mrs. Wang when he heard Duan Zhengchun say so.
finally, Duan Zhengchun changed his mind to ask Mu Rongfu to kill Mrs. Wang because Duan Zhengchun saw Mrs. Wang's sad appearance and remembered their previous events, so he forgave Mrs. Wang in his heart and changed his name to Mu Rongfu to kill Mrs. Wang. His purpose was to make Mu Rongfu suspicious and let Mrs. Wang go.