If you afe really keen on Phuket then go to the north of the island (near the airport). The Indigo Pearl is nice and there is a mariott in the area too. Quiet area, no night clubs, small restaurants on the beach, not sleazy at all.
I'd also recommend staying clear of that area. Unfortunately seedy bars are legion pretty much everywhere on the high streets and beaches.
The northern shore (from Surin and traveling north towards Phangan bay & Krabi) is much better but you'd be resort bound. Its more upmarket and downright trendy around Surin.
Agree Krabi and Koh Lanta have a laid back feel and are more conservative areas so getting out of the resort and eating locally is a nicer experience with kids.
Koh Samui is really nice but weather is best may/september
If you want great beaches and local life try Hoi Ann in Vietnam. Miles of pristine beach, tailboats and day trips to local islands and a lovely conservation town for evening dinners. Car free and super kid friendly. Lots of local artists, tailors night market and delicious restaurants. You'd have to fly via Hanoi or Ho chi Minh or singapore.
Avoid Phuket/patong beach, karon beach unless you like wandering amongst a market place of prostitutes. It is so in your face. We first went 20 years ago, 3 years on the trot, and loved it. Returned 4 years ago and counted the hours till we left. Any time DH was alone, he was approached by young girls offering to screw him for £10...and when he declined offered him 'younger' girls You are surrounded by 60 year old Western European men walking round with (hopefully at least) 16 year old Thai girls, taking them to bars, and earning. Commission from the Mamas who run the bars. Sure there are some pretty places in Thailand, but I would rather not spend money in a country whose government are very aware of what goes on, but are loathe to stop it as sex tourism brings in a Lot of money for the economy. Phuket nightlife