You already have a calendar table, great!
The you don't the table of numbers I talked about - the calendar table is an extension of that concept.
I think this should work:
SET DATEFIRST 7
UPDATE CalendarTable
SET NewWeekCol = datepart(week, CalendarDate) -
datepart(week, datename(YEAR, CalendarDate) + '0401') + 1
WHERE month(CalendarDate) BETWEEN 4 AND 9
But note that since I don't your table, I cannot test. But you could tweak it on your own.