A 3-year old on a plane needs constant entertainment. I can tell you that from personal experience. My son (now 19) has a touch of ADD, so I wasn't dealing with an abnormally perfect child and he wasn't on medication. We dealt with plane flights with books, small toys, snacks, etc. I also conceded the window seat to him. It's a full-time job but I remember only a few seat-kicks in his flying career.
I have a nephew who was a very physical, active little boy from Day One. His mother had to fly from CLT to Florida with his sister and without my brother (her husband). She got the doctor to prescribe a mild tranquilizer. Worked like a charm. Unfortunately, it wore off because they didn't have a landing slot. As they circled the airport and the kid started climbing the walls, the FA asked my sister-in-law if she could calm him down. She told them it was their problem- they didn't land on time!
As I write this, my nephew (now 13) is in Australia, representing the US in a major swimming competition. Guess the drugs had no lasting effect.