As explained, it is not possible to do what I want with JPA, so I employed the hibernate.cascade annotation, with this, the relevant code in the Parent class now looks like this:
@OneToMany(cascade = {CascadeType.PERSIST, CascadeType.MERGE, CascadeType.REFRESH}, mappedBy = "parent")
@Cascade({org.hibernate.annotations.CascadeType.SAVE_UPDATE,
org.hibernate.annotations.CascadeType.DELETE,
org.hibernate.annotations.CascadeType.MERGE,
org.hibernate.annotations.CascadeType.PERSIST,
org.hibernate.annotations.CascadeType.DELETE_ORPHAN})
private Set<Child> childs = new HashSet<Child>();
I could not simple use 'ALL' as this would have deleted the parent as well.