Yes, the son of Yi Guipin in Joy of Life was the Third Prince, Li Chengping.

Yi Guipin's son was not the Crown Prince. The Crown Prince was the son of the Empress.
Yi Guipin was the Qing Emperor's concubine. She was the birth mother of the Third Prince, Li Chengping. Yi Guipin had deep feelings for the Third Prince and played an important role in the drama. She supported Fan Xian and had the Third Prince take Fan Xian as his master, hoping to help him grow. During the Jingdou rebellion, Yi Guipin had always stood by Fan Xian's side. She had become the winner of the Palace and was in charge of the rear palace. The role of Yi Guipin was played by Deng Tongtian and Sui Junbo respectively.
Joy of Life Yi Guipin's son was called Li Chengping.
Joy of Life Yi Guipin's son was called Li Chengping.
In Joy of Life, Yi Guipin's son was called Li Chengping.
Joy of Life Yi Guipin's son was called Li Chengping.
In Joy of Life, Yi Guipin's son was called Li Chengping.
In Joy of Life, Yi Guipin's son was called Li Chengping.
In Joy of Life, Yi Guipin's son was Li Chengping.