I've been to Turkey a number of times and had nothing but positive experiences (except when driving - they make the average Roman motorist look positively saintly)...
I've had friends who went to a Neilson place on Ardaykoy Island near Marmaris with their kids. Absolutely loved it.
Depending on how old the kids are and their interests, I'd also consider Istanbul (seriously - it's a fabulous city) and Gallipoli.
Ever tried Alanya ?
Small city, big town, fabulous beaches (sandy) with waves that crash in in the first 10ft, calm beyond that..great fun to get thrown about a bit if you like a bit of excitement, but quite safe.
Town is really quite large, it has its touristy shopping market but loads of cheap local authentic shops within a short walk. Good harbour, buzzing at night. Woodland/river parks a few miles away (Dim Cai) plus large caves a few miles from that (Dim Mergasi). I didn't have any problems driving there, just need to be alert.
Not many Brits there, you won't hear much English spoken, lots of Turkish holiday there plus Scandanavians.
It was so good we broke the habit of a lifetime and went back there twice (mostly due to the hotel , the Grand Okan)
Three visits to Turkey, never had a bad experience.