This morning my family and I were in an unfortunate situation and I'd like to see what the BA board thinks of my options/rights in this case.

My family was booked on the 10h RTM-LCY flight operated by BA Cityflyer. As Rotterdam is a small airport, like LCY, they planned to arrive at 8:15 which would leave plenty margin. However, for some reason the motorways were in total gridlock this morning, much more severe than even rush hour, which turned a 1-hour drive in about a 2,5 hour drive. At some point I got a call they estimated they would miss their flight.

As soon as the Dutch customer service center opened at 9h, I called and asked if they could be rebooked onto the 10:55h flight. Seats were available but the agent quoted a hefty amount of €400-500 for the fare difference and change fee.

I then came across article 3c4 of BA's conditions of carriage which states:
In my opinion the severe traffic and resulting extraordinary delay was beyond my family's control so this term would apply. I thus advised the agent of this condition and appealed for a rebooking without a recalculated fare. After some discussion this was escalated to a supervisor. He said he could waive the change fee but that the fare would have to be recalculated. He did not address the CoC condition or stated that it would not be applicable.

My family was not willing to pay this hefty fee for a short leisure weekend so then my next idea was to book them on an Avios redemption on the 10:55h flight. I discussed this with the supervisor to arrange that they could still use their return flight. He told me he could alter the ticket to a one-way by cancelling the RTM-LCY flight and that there would not be a charge in that case. So I gave the go ahead.

In the meantime it was almost 10h as the discussion took some time. Apparently in the time I arranged the rebooking on the phone, my family had miraculously arrived at RTM, rushed through security and the flight was still waiting for them. So when I got off the phone with BA, I got a text they were actually already on the plane. Great, I thought. So I did not finish the Avios booking. However some minutes later I got another text that the plane had taxied out but returned to the gate due to a passenger list discrepancy and they were offloaded. The airport staff then also quoted a hefty recalculated fare to be booked on the 10:55h flight. I tried to book using Avios but it was already so close to departure, this was not possible any more. Only Club Europe seats on the 15:45h flight was available. As my family was in despair, I booked this flight for them. This cost me more Avios and most unfortunately, my family over 5 more hours of their trip.

I acknowledge that it is not BA's fault that my family originally missed their flight. However I also think their delay was beyond their control as they took a very reasonable margin for arriving in time at RTM airport.

My issue is that a lot of inconvenience, lost time and less importantly Avios could have been saved in case the rebooking was done free of charge in accordance with BA's CoC.

So do you think I am right in appealing to this clause and BA should have rebooked my family without re-adjusted fare? Is there any possibility to recover (part of) the Avios I spent myself to get them to London instead?