U can get a phone no. from the agent first and then call the agent to book the local tour on phone. U can bargain w/the agent. I took the tour half day tour to the egg island a few days ago, 2A1C (7 yr old), total 2300 Baht,ca including transport to and from Kata Beach. You bargain for a lower price as ur kid is just 3 yrs old but the agent may charge u additional costs for transport as Mai Kao Beach is really far far away from the pier.
I found that the tour to the egg island was always arranged in the afternoon.
Mao Kao Beach is very quiet, so better get your supplies (drink, snacks, etc) b4 u check in the hotel. better arrange a car for travelling to other places, eg. Central Festival.
Book the local tour after u arrive in Phuket. U can get the phone no. of the agent for booking or book the tour in person at Patong, kata, karon beaches.
Get free cell phone sim cards at the airport. The sim card includes a 7 baht value which can give u 2-3 short local calls. Top up the value at 7-11. 50 Baht will be ok. The sim cards can also be used in Bangkok.