According to the information you provided, the sea view room booked at Le Méridien Phuket Beach Resort shows that it can only accommodate two people. Typically, hotels will charge based on the maximum occupancy specified in the room. If your group is two adults and a 9-year-old child, it is theoretically possible because children are not usually counted as additional guests.
As for whether children need to be charged extra, it depends on the specific policy of the hotel. Some hotels provide free accommodation for children under 12 years old, while others may charge a fee for additional children. It is recommended that you contact the hotel customer service directly to inquire about the specific fee policy for children to stay in order to get an accurate answer. This way, you’ll know if you need to pay extra for a child.