It looks like you've got a one to many relationship set up just fine. The problem I've found as a newcomer to Hibernate is that if you get away from a easily defined "id" in your entity then mapping things seems to become exponentially harder.
In my entities always using <id> (usually a simple integer sequence or auto-increment in MySQL) as well as a <natural-id>. Anyway, since you can't change PARTS I'd consider making that a component instead of an entity.
Maybe a mapping in your Car entity like this might work... (I haven't tested it so my XML might be a little off)
Code:
<set name="parts" table="PART" cascade="delete" >
<key column="CAR_ID"/>
<composite-element class="foo.bar.PartComponent">
<property name="sequence" column="SEQUENCE" type="int"/>
<property name="name" column="NAME" type="string"/>
</composite-element>
</set>