How do I map a child object using one of the parent object propeties

If your child object properties defined on run time do not map it.

You will end up with unwanted mappings which can be a headache later. Instead you can map whatever the stable parent (as you mention).  In run time you can call child object using parent. For eg there are two unique parents X and Y but both have a child call z, you can call X.z or Y.z depending on your requirement.