[CentOS] bash job control and signals

I want to suspend a script using a signal but that does not work as I want. I made an example script:

$ cat script #!/bin/bash echo $$ gkrellm

If run this script gkrellm starts up and I can use job control from the terminal to suspend the script (CTRL-Z) and resume it (fg or bg). If I suspend I can see that gkrellm freezes (that's why I choose gkrellm in this example):

$ ./script 23632 --CTRL-Z-- [3]+ Stopped ./script $ fg ./script

Next I want to do exactly the same but from another terminal using a signal:

kill -SIGSTOP 23632

[3]+ Stopped ./script

So the bash script is indeed suspended, but the gkrellm keeps running. I can of course signal SIGSTOP to gkrellm and then this gkrellm will suspend as well. I have however an application that suspends my script and I cannot change this application. I want all processes that are children also to become suspended. I tried to add a trap, but that did not work.

Any idea how to make this work?

Theo