Typically you'd put your cascade attribute on the collection, not the child object, so this:
Code:
<bag name="Children" table="children" inverse="true">
<key column="ParentName"/>
<one-to-many class="nHibernateRelationship.Child, nHibernateRelationship"/>
</bag>
becomes
Code:
<bag name="Children" table="children" inverse="true" cascade="all">
<key column="ParentName"/>
<one-to-many class="nHibernateRelationship.Child, nHibernateRelationship"/>
</bag>
That's the only thing I can see in your mappings that is off.
You can read more here at
http://www.hibernate.org/hib_docs/v3/reference/en/html_single/#example-parentchild-cascades