Yes going through the options dialog wouldn't use those commands since the order of multiple is being changed and not committed until OK is clicked. You should be able to use the CollectionChanged event of the Groups collection to determine that the collection has changed however it seems that this is not firing in this case. I have logged an internal issue for this. You should contact the support group and reference issue #13997 so you can be notified when this issue is addressed. At that point you can use the CollectionChanged event to get a notification when the order is changed.
I believe you can hook the ExecutedCommand event and look for a command of OutlookBarCommands.GroupMove(Down|Up)Command.