My daughter will be staying with my son who lives and works in shanghai.

The sponsorship letter may be needed if your daughter will stay for a long time in PRC.
The reason why the information of 144 hour policy is unavailable on the embassy website may be because the embassy doesn’t update the relevant information in time. Or it is because the 144 hour free transit is only available in Shanghai, Zhejiang and Jiangsu, which is not widespread.