Mytrip.com complaint: Unable to get on flight due to ticket not being issued for a passenger

I booked my tickets back in May 2019 on Mytrip.com (Order number: KWG4EN). I was traveling with my mother, my wife and two infants under the age of 2.
After receiving the travel document, I received no further emails from MyTrip about any changes.
When I arrived at the airport to check in, the airline could find no record of the outbound leg of the booking using the airline references on the travel document (TSTNBW, UYW7UY). They could only find the inbound leg. Also using our surnames they could only find record of an inbound flight on record but no outbound flight. The airline told me to contact my agent.
I called MyTrip from the airport, hoping to resolve this before the check in closed. However, after being disconnected twice and being on hold for an hour, the MyTrip phone operative told me that everything was fine on their end and they could see details of my booking ed for the flight. So I went back to the check in desk to try again, but they still could not see any booking. So I again called MyTrip and remained on hold for an hour, only to be told by the MyTrip phone operative that my booking had been cancelled by the airline.
Why was I told this now, when just one hour ago on the previous phone call, the operative said everything on the booking was fine? And if everything was fine, then why couldn’t the airline see my outbound booking? And if my booking was actually cancelled earlier, why didn’t MyTrip inform me?
After all this, the check in had closed, and we missed our flights. My two infants suffered a lot as a result of this, as well as my wheelchair bound mother. We were out from 8am in the morning and remained in the airport for 6 hours. We had to buy food at the airport which cost us £20 and my children were restless and crying. My brother and my dad who had brought us to the airport had to pay over £40 for airport parking.
We had to book whatever one way flights we could find to travel the next day, but the only suitable flights we could find were from Birmingham airport 100 miles away. So we had to arrange transport for all of us to Birmingham which cost us over £300. In total my infants were without rest for 48 hours. The journey was also very difficult as we were unable to book bassinet seats due to the last minute booking.
After I returned I contacted Turkish airline to investigate what exactly had happened. They replied saying that MyTrip failed to issue the ticked for one of the passengers and thus the flight was removed.