With a query like this (simplified for clarity):
SELECT \'East\' AS name, * FROM events WHERE event_timestamp BETWEEN \'2015-06-14 06:15:00\' AND \'2015-06-21 0
Wrap it in a derived table (which is what "HINT: .... or move the UNION into a FROM clause" is suggesting)
select * from ( ... your union goes here ... ) t order by CASE WHEN name='East' THEN 1 WHEN name='West' THEN 2 WHEN name='Both' THEN 3 ELSE 4 END;