April is the hot season. If you hate heat you might want to go a couple of moths earlier.
I'd swap the 2 nights at Phuket for some time in the north. It's very differant from the south and there is far more to Thailand than islands and beaches. The cuisine in the north is differant and you could hire a motorbike for a couple of days to do some day trips around the Golden Triangle. The elephant nature park in Chiang rai is probably the best elephant tourism in the country because they let the elephants be elephants instead of football players etc (although I will admit to a soft spot for the elephant artists).
IMO Phuket is overcrowded and over touristed although there are quieter areas.
Maybe you could consider spending a bit less time at the beach resorts and some more time in the jungles but if you like the beach and don't like jungles that would be pointless.
Your itinerary seems pretty logical to me but I don't think there's any such thing as the right order - that said my prferred method of travelling is to turn up at the train/bus/ferry and cath the next one regardless of where it's going (unless I've been there recently) and obviously you like to travel in a fairly structured way so I'm probably the last person you should listen too .