Delay to AF165 rebooked but booking incorrect
Myself, wife and 2 young kids booked on AF165 leaving 17/7 (in a few hours) but flight delayed 1:20 due to technical reasons on incoming aircraft. Received email last night. Contacted Air France service desk in US (Fr and Th did not answer) as I would miss onward connection. Agent rebooked to TG this evening, 16hrs later. Bad but better than alternative of spending night and half of tomorrow in Paris. All good so far and a good result after 90 minutes on th phone.
Tried checking in online with TG but my ticket bounces, other 3 passengers ok. Unfortunately a mistake was made in rebooking, TG say there is a booking for 4 seats but only 3 passengers and 3 ticket numbers attached. They say they will refuse to honour travel for the missing passenger, myself.
Called US service centre 3 times, they insist my ticket is valid, there is a ticket number and it shows on their system. They even reissued ticket with new ticket number but problem still exists. Called Thai 3 times and they can see ticket but insist booking still has only 3 out of 4 passengers specified and ticket number and passenger details missing. They say they cannot add and issuing carrier must correct booking.
To make matters worse, I did not realise Air France US service desk is handled by DL, so ticket originally issued on AF is reissued on DL stock.
It has taken over 5 hrs and everyone seems to think it it is the other's problem. Am now at a loss on how I can travel. What can I do?
Wondering if a solution would be to just book a new ticket on my own money and claim back from AF but I am afraid they will reject the claim and I will be severely out of pocket. A last minute one way on premium economy to Europe on TG does not come cheap, so it is a big risk.