One of my close friends had her daughter (on your age) at BCIS and they were very satisfied with the school and educational program.
Regarding the good housing alternatives near the beach, I can give you first hand advice and assistance. I am working for a relocation company doing both removals and house hunting in the major cities in Thailand.
Would appreciate if you could drop me an email on "stein (at) united-relo . com" with more details regarding your requirements (villa/apartment, budget) and I would then be able suggest more exact alternatives for you. There are many big expat areas in Phuket as well as many beach areas. I presume you would prefer to stay away from the main tourist areas??
I would definately recommend you to rent/buy a car as there is no real taxi service like in Bangkok down there. Taxis in Phuket is mainly these small cars where you have to sit in the back and normally they charge tourist prices..... Get yourself a car no matter what!! Make sure you have an international driving lisence to avoid troubble with the police etc.
Please drop me an email on the above address and I will provide more exact information accordingly.