I think Samui is only serviced by BKK air though Mr D..
So if it is Patts - Samui - Phuket - BKK the first three places (2 flights) need BKK air..
One hell of a tour there
Look into when the full moon party is on Kho Phan Gan and try to be on Samui at that point.. Probably enjoy seeing it the once.. Will want a healthy budget for that tour I would think..
Personally I would cut down the BKK trip (3 or 4 days and I have enough of it.. I am just not so into the city) and keep Patts to a short leash also and have more time on Samui and Phuket.. Both places have a lot of charm for me. Really depends on how much your here for girls and gogo scene and how much for beaches and nightclubs scene..