Update trigger doesn't see parent field of hierarchical

I have an object with an hierarchical relationship. I have a trigger on this object that has On Create/On Update/On Finalize. This trigger looks at the parent relationship.

When I create a new object from inside the parent object by clicking the + sign after the list of child objects, the trigger does fire, but doesn't see the value of the parent relationship.

An example:

• I have an object named group with a hierarchical relationship to itself, so I can nest groups;
• I create a new group;
• I edit the group. From the list of child groups, I click +;
• I create a new group there. Notice that the parent group is not set, even though the new group will be added as a child group to the group I just click the +;
• I save the new child group;
• The child group appears in the list of children in the group I started from;
• I save the parent group.

What happens is that the trigger does not see the parent group. If I edit the new child group, I do see the parent group set. If I then save the child group, the trigger fires again, and it does see the parent group.

How can I make the trigger see the parent group the first time around?