What is the shortest/fastest route from Gatwick to Antalya if we divide our journey into 2-hour direct flights
score:10
I'll assume nominal flight times are what you're looking for, and take them from www.flightconnections.com.
I also assume that you're concerned about the effect of a long journey on a small child, from hints in the question. While two hours travel time is often-quoted and may be your preference, it's far from a hard limit. By stretching it a tiny bit on one leg, you can save a whole flight. Anyway, your Sarajevo leg is 2:15.
I looked at destinations from Antalya (AYT) as close to 2 hours as possible, heading in the right direction. Bucharest (OTP) is 1:55, so that's a good start. From there I suggest relaxing your criterion by just 5 minutes - OTP-MUC (Munich) is 2:05, then MUC-LGW (Gatwick) is 2:00. Alternatively OTP-VIE (Vienna) is 1:45 and VIE-LGW is 2:05.
Instead of Bucharest, you can go via Skopje (SKP), also 1:55 from AYT. Then it's 2:10 to Zurich (ZRH) followed by 1:40 to LGW. SKP doesn't share many destinations with LGW, and you may as well end up the right side of London rather than come into one of its other airports.
I haven't tried to turn any of these routes into an itinerary, or cost them, because I don;t know how much downtime you want between flights.
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