Hello OP,

Sorry to hear about your troubles on your flight.

What is likely happened is that as your flight was delayed in arriving to DXB, but still within the minimum legal connection time at the airport, they expected all passengers to head to the gate as soon as possible. Whilst I understand you had more pressing issues to attend to with your children, unfortunately EK had already made the decision, as you did not present yourself at the gate within their time limits, to offload you and rebook you on the next service. Although the flight did not actually leave the stand until later, that would be because they would have to locate your bags and offload them which would have delayed that flight.

Most tickets, especially cheap ones, have stiff penalties for not turning up without cancelling - that would be the no show fee, a fee you would have to pay before rebooking on EK. This may have been the 800 USD you paid, but even that sound steep. Do you happen to have any documentation for these charges? This incident happened in 2014, so I am unsure as to why you did not raise the issue either with EK or Chase sooner after this happened, as it seems to have been quite a serious one for you - leaving a claim or an issue this long to raise with the airline and issuer I'm afraid might weaken your case for any customer service gestures they might be willing to give you in this case.