Previous Monday & previous Sunday’s date based on today’s date

Easy:

--start of last week
SELECT DATEADD(wk, DATEDIFF(wk, 6, GETDATE()), 0)

--end of last week
SELECT DATEADD(wk, DATEDIFF(wk, 6, GETDATE()), 6)

EDIT:

The below will handle the Sunday date issue.

DECLARE @input varchar(10)
--SET @input="9/9/2012" -- simulates a Sunday
SET @input = GETDATE()

--start of last week
SELECT DATEADD(wk, DATEDIFF(wk, 6, 
CASE DATEPART(dw,@input)
WHEN 1 THEN DATEADD(d,-1,@input)
ELSE @input
END
), 0)

--end of last week
SELECT DATEADD(wk, DATEDIFF(wk, 6, 
CASE DATEPART(dw,@input)
WHEN 1 THEN DATEADD(d,-1,@input)
ELSE @input
END
), 6)