What is the shortest/fastest route from Gatwick to Antalya if we divide our journey into 2-hour direct flights

We intend to air-travel from East Sussex to Antalya. What is the fastest route if we divide the journey into 2-hour direct flights?
I randomly picked Frankfurt and Sarajevo as places to break the journey, but I would like to avoid Bosnia and Herzegovina because of their requirements to travel with children.
Travelling with children
Children under 18 years of age who are not Bosnian nationals and who are travelling unaccompanied or accompanied by an adult person other than their parents must carry a notarised letter from their parents giving permission for the child to travel. The name of the accompanying adult must be clearly stated. If the child is accompanied by one parent, particularly if the parent has a different surname to the child’s, the accompanying parent should carry a notarised letter from the other parent giving permission to travel.
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Trip Report of the TUI 787-9 | London Gatwick to Antalya | My first dreamliner flight!
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