The second prince in Joy of Life, Li Chengze, was not the princess's son. In the play, the princess had an affair with the crown prince and formed an alliance with the second prince, but they did not have a child. Therefore, Joy of Life did not mention that the second prince was the princess 'son.

The second prince in Joy of Life, Li Chengze, was the son of the eldest princess, Li Yunrui.
Yes, the Crown Prince of Qingyu was the Empress's son. The Qing Emperor's Crown Prince was the Empress 'eldest son, and the Empress was the Qing Emperor's biological daughter. This meant that the Crown Prince was the Empress's child, which was more legitimate than the other princes.
The son of a princess was not necessarily a prince. The term 'prince' was usually used for the heirs of princes, not ordinary princesses. The title of the princess's son depended on their father's title. If their father was a marquis, then their son would be called a young marquis, and if their father was a duke, then their son would be called a young duke. Therefore, the son of a princess was not necessarily called a prince.
The Crown Prince of Joy of Life was the Qing Emperor's second son.
Crown Prince Qing Yunian was the Qing Emperor's second son.
In Joy of Life, the eldest princess and the crown prince did not have a son.
The Crown Prince of Joy of Life was not the third son. The Crown Prince was the Qing Emperor's eldest son, and the Third Prince was Li Chengqian. He was the legitimate son of the Empress and was independent of the status of a prince. Therefore, the Crown Prince and the Third Prince in Joy of Life were different characters.
The Crown Prince of Joy of Life was not the third son. The Crown Prince was the Qing Emperor's eldest son, and the Third Prince was Li Chengqian. He was the legitimate son of the Empress and was independent of the status of a prince. Therefore, the Crown Prince and the Third Prince in Joy of Life were different characters.
The Crown Prince in Joy of Life was not the Third Prince. The Crown Prince was the Qing Emperor's eldest son, and the Third Prince was Li Chengqian. He was the legitimate son of the Empress and was independent of the status of a prince. Therefore, the Crown Prince and the Third Prince in Joy of Life were different characters.
There were different opinions on whether the Crown Prince was the third child in Joy of Life. Some documents stated that the Crown Prince was the Third Prince, while others believed that the Crown Prince and the Third Prince were different people. Therefore, it was impossible to determine if the Crown Prince in Joy of Life was the Third Prince.