For background information, it might be worth reading (on Linux) man 7 signal.

When you hit CTRL-C then a SIGINT is sent to all the processes in the foreground group. When you use the shell built-in command kill the shell will send SIGTERM. If you are getting different behavior with different signals then someone must be trapping the SIGTERM. Ignore signals are usually inherited.

In addition, usually, when a parent dies it sends a SIGHUP to the child, which might kill the child, again depending on signal handling, for example using the nohup program or trapping SIGHUP will prevent this.

Keeping track of PIDs should not be difficult, it is the return value of fork in the parent. Provided the children of B are not ignoring hangups, then killing B should bring the children down as well.

Alternatively, from kill:
"Unlike in the shell, if SIGNAL is negative, it kills process groups instead of processes."
Provided the children have not switched process groups (which a daemon might do) then that might be a safer bet. It is not worth calling a shell's version of kill using system when there is one built-in to perl.