The direct answer is to call FamilyInstance.GetSubComponentIds(), and filter them for the desired child family instances.
If you can collect the child families directly via a standard FilteredElementCollector though, I suggest that route. And if identifying the parent is necessary, find it by walking up the family tree. Here are some helpers I use for this very scenario.
public static bool IsNested(this FamilyInstance instance)
{
var isNested = instance.SuperComponent is FamilyInstance;
return isNested;
}
public static bool IsTopLevel(this FamilyInstance instance)
{
var isTopLevel = instance.SuperComponent == null;
return isTopLevel;
}
public static FamilyInstance GetParent(this FamilyInstance instance)
{
var parent = (FamilyInstance) instance.SuperComponent;
return parent;
}