Use esta solução:
SELECT SUM(
CASE WHEN a.Start_date = b.min_sd AND a.Start_date <> b.max_sd THEN
(DATEDIFF(a.End_date, '2012-08-30')+1) * a.Price
WHEN a.Start_date = b.max_sd AND a.Start_date <> b.min_sd THEN
DATEDIFF('2012-09-04', a.Start_date) * a.Price
WHEN (a.Start_date,a.Start_date) IN ((b.min_sd,b.max_sd)) THEN
(DATEDIFF('2012-09-04', '2012-08-30')+1) * a.Price
WHEN a.Start_date NOT IN (b.min_sd, b.max_sd) THEN
(DATEDIFF(a.End_date, a.Start_date)+1) * a.Price
END
) AS totalprice
FROM rooms a
CROSS JOIN (
SELECT MIN(Start_date) AS min_sd,
MAX(Start_date) AS max_sd
FROM rooms
WHERE Room_type = 'luxury' AND
End_date >= '2012-08-30' AND
Start_date <= '2012-09-04'
) b
WHERE a.Room_type = 'luxury' AND
a.End_date >= '2012-08-30' AND
a.Start_date <= '2012-09-04'
Substituir ocorrências de
2012-08-30 e 2012-09-04 com suas datas de início e término de entrada, respectivamente. Isso levará em conta as datas de início e término no mesmo mês, além de abranger vários meses.
Demonstração do SQLFiddle
