create table t (t1 int, t2 int)

insert t select 1, 2

select * from t
t1          t2          
----------- ----------- 
1           2

alter table t add placeholder int

update t set placeholder = t1

update t set t1 = null

exec sp_rename 't.t1', 't3', 'COLUMN'

exec sp_rename 't.placeholder', 't1', 'COLUMN'

select * from t
t3          t2          t1          
----------- ----------- ----------- 
NULL        2           1

--Create the table to fix this awful nightmare of a situation
CREATE TABLE djl_test_colid(
	int1 INT,
	int2 INT,
	value VARCHAR(55),
	int3 INT)

INSERT djl_test_colid(int1, int2, value, int3)
	SELECT 1,2,'Here''s the problem',4

SELECT * FROM djl_test_colid

--Notice that the colid is what "physically" orders the table.  
---Because of this, you have to recreate the table to reorder, which is what EM does.
SELECT
	so.name,
	sc.name AS column_name,
	sc.colid
FROM 
	sysobjects so 
	INNER JOIN syscolumns sc ON so.id = sc.id 
WHERE 
	so.name = 'djl_test_colid'

--The other option is to muck around with the system tables, which I highly recommend against.
UPDATE sc
SET colid = 
	CASE
		WHEN colid = 3 THEN 4 
		WHEN colid = 4 THEN 3
		ELSE colid
	END
FROM
	sysobjects so 
	INNER JOIN syscolumns sc ON so.id = sc.id 
WHERE 
	so.name = 'djl_test_colid'


SELECT * FROM djl_test_colid

--Notice now that everything is right in the order of orderdom.
SELECT
	so.name,
	sc.name AS column_name,
	sc.colid
FROM 
	sysobjects so 
	INNER JOIN syscolumns sc ON so.id = sc.id 
WHERE 
	so.name = 'djl_test_colid'

--Clean up after yourself.  gheesh
DROP TABLE djl_test_colid

CREATE VIEW MyView
AS
SELECT
  MyCol1,
  MyCol2,
  MyNEWCol,
  MyCol3,
  MyCol4
FROM MyTable