Keith, there are NO direct ferry services from Italy to Turkey now the last service stopped in 2010 and will not be replaced.
There is a ferry from Venice, Anccona, Bari, Brinsdisi to Greece Igoumenti, Patra. then take the land brige to Piraues (200km) then take a 2nd ferry to Chioes and then hop from there to Cesme or take a third ferry from Piraeus to Rhodes then the highspeed Cat to Fethiye
Or travel on Ryanair from London Stanstead to Anccona or train from London to Athens or Venice the train from London to Athens takes 2 nights hope you got plenty of time, you will have to work out the cost once you know your route etc, but it should be an exciting trip the.... kids would love it.