To clarify exactly what is being asked, PARENT task and CHILD task are both in SSM. CHILD is internally started by PARENT so its IPL_STATE=IPL and PREREQ=PARENT. Upon system shutdown, you need to stop PARENT, leaving CHILD UP. If that is the case, then yes, you would accommodate this request via the REFMODE or PREMODE columns.
First to clarify these columns:
The PREMODE setting tells SSM how to perform prereq or subreq processing for the resource that is being processed. Meaning, if the current state is (CS=DOWN) and desired state is (DS=UP) for the PARENT, SSM internally would do prereq checking based on the setting of its PREMODE value. If PREMODE=PREREQ is for PARENT, then SSM only would check to see if the PREREQs for PARENT are UP and with PREMODE=PREREQ for the PARENT, when you go to shutdown it down (CS=UP DS=DOWN), SSM would not check for subreqs (it would ignore any other resource like the CHILD that is PREREQ=PARENT). So, this is one setup that would do what is being asked - Setting PREMODE=PREREQ for PARENT only .
The REFMODE setting tells SSM how to process a resource when it is being REFerred or looked at as a prereq or subreq when SSM is processing some other resource. Meaning, if you attempt to stop the PARENT task CS=UP/DS=DOWN, SSM would look at or refer to all other SSM resources that have PREREQ=PARENT. Then, based on the REFMODE of that referred resource (the CHILD in this case), SSM would check its current state (CS) to make sure it is DOWN, since you are requesting to stop the PARENT. But, if the REFMODE=PREREQ for the CHILD, SSM would ignore since REFMODE=PREREQ means only process the CHILD in prereq conditions. So, another method you could do here to get the PARENT to stop without shutting down the CHILD is to set the CHILD resources REFMODE=PREREQ.
The technique chosen depends on whether or not you have other resources outside of the PARENT CHILD that might be prereqs/subreqs of these tasks. The best way to easily see what/how SSM processes resources with these different mode settings is to simply insert 2 two dummy resources into the table (like PARENT and CHILD) and then just set the CS/DS DOWN/UP with different MODE settings.