All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His Slave and Messenger.
The Hadeeth you have mentioned, dear Brother, is an authentic Hadeeth that was reported in both Al-Bukhari and Muslim as is the highest level of authenticity. It was narrated on the authority of Abu Hurayrah . As for the meaning of "a half child," it means a premature or disfigured child. Some versions of the Hadeeth read, "except one who delivered a half person."
Allaah Knows best.