We went to Thailand last year with a 6 and a 4 year old. We stayed at Koh Samui in the Centara Grand Beach Resort. Hotel was fantastic, we had a suite with our own little pool which was really good when the kids needed some quiet time or if DS fell asleep (didn't happen very often!). We spent a lot of time around the pool and on the beach. The resort is beachfront so we could do both at once! I really wanted to see the elephants but we never got around to it.

We stopped in Thailand on the way home from a month in Europe, we did fly Thai and had no problems with the airline. If transfers aren't included with your accommodation I would definitely pre-book them to and from the airport. The cost is usually very reasonable and you won't have to mess around with a taxi.