It always helps to know what Shell you are running.

I think that the unix "tee" command can be used to achieve the desired effect providing that every child log is written to by a unix Shell redirect (i.e. not directly by a program). The unix "tee" command splits the input from a pipe into two directions (like a tee-piece in plumbing).

Code:

echo "Log entry" | tee combined.log >> child.log

This approach is not suitable for high-intensity logs or mission-critical logs because Shell is not 100% reliable with concurrent writes to the same file.
The technique is very good for creating a central server log of say service ups and downs.