If you querying a SQL Server database CASTing the columns to datetime values should work. If MGMNT_UPDATE.Date holds a string value then you probably want to indicate that in the column name to avoid confusion, e.g. MGMNT_UPDATE.DATE_STRING.
select * from "MGMNT_UPDATE" where CAST("MGMNT_UPDATE"."Date" AS DATETIME) >= '3/20/2013' and CAST("MGMNT_UPDATE"."Date" AS DATETIME) <= '3/20/2013' order by "MGMNT_UPDATE"."Date", "MGMNT_UPDATE"."Time" DESC;
I can't test the above, so if it does work, try CASTing the date literals.
select * from "MGMNT_UPDATE" where CAST("MGMNT_UPDATE"."Date" AS DATETIME) >= CAST('3/20/2013' AS DATETIME) and CAST("MGMNT_UPDATE"."Date" AS DATETIME) <= CAST('3/20/2013' AS DATETIME) order by "MGMNT_UPDATE"."Date", "MGMNT_UPDATE"."Time" DESC;
By the way, I suggest you use aliases in your SQL to reduce the length of the statements (if only for the sake of your fingers). By using underscores in your table and columns names (and any other DB objects) rather than spaces, you can avoid needing to type double quotes everywhere.
select *
from MGMNT_UPDATE A
where CAST(A.Date AS DATETIME) >= '2000-03-20'
and CAST(A.Date AS DATETIME) <= '3/20/2013'
order by A.Date, A.Time DESC;
Next, you might want to uppercase only SQL keywords and leave everything else lowercase.
SELECT *
FROM mgmnt_update a
WHERE CAST(a.date AS DATETIME) >= '2000-03-20'
AND CAST(a.date AS DATETIME) <= '3/20/2013'
ORDER BY a.date, a.time DESC;