Interesting, two points.
First up, a death occurred. Standard international protocol is note the position it happened if inflight. In this case it would appear the baby was alive at touchdown so that would be classed as a death in Kazakstan. Again, protocol requires an autopsy from the authorities certifying the death, Kazakstan. Most unusual to be able to depart with the body onboard. Cause of death has to be determined by the authority where the death occurred. This knowledge comes from experience and exposure to the requirements over 26+ years of doing this. Only once because a special case situation, which was put to the authorities, was a body allowed to stay onboard for further flight and that took several hours of negotiation at senior Government level and a crew change.
Secondly, the FTL calculations and justifications for a second sector to HKG are wrong and ultimately this WILL be classed as an illegal operation. The crew should quite rightly be worried. My understanding is one crew member has already contacted the AOA as he is now very nervous about the situation. What on earth was wrong with either saying "under the circumstances it would inappropriate to continue to HKG" or "we have sufficient duty time available to proceed to XXX" (possibly PEK) were another crew could have been sent expeditiously to recover the operation?
In the previous year I've come across the situation were I've been asked would I consider discretion and the reply "under the circumstances it would inappropriate to continue" has terminated the conversation and we have taken appropriate rest before continuing. It is NOT difficult! Never has it been question. The company also know the rules.