Product: Credit card

I booked a flight for travel for me, my wife and our XXXX kids using Chase 's XXXX XXXX, which offers additional benefits for my ~ {$550.00} annual fee credit card. The price shown when selecting flights on the portal was the same price shown on Southwest, so I opted to book with Chase. After purchasing, I realized Chase had added about {$55.00} in additional fees to the ticket, so the price was now {$55.00} more than the Southwest price. Given I had already booked the flight, this was frustrating to see the increase in price. Further making matters worse, when I went to check in for the flight, I noticed our names were not entered properly on the Southwest webpage, despite appearing normal on the email confirmation I received from Chase. Additionally, my XXXX XXXX XXXX ( XXXX ), was also not applied despite entering it with Chase. I called Southwest to fix the issue, but they said since Chase booked the ticket, they 'own ' the reservation and I have to contact them directly. So, I called Chase, waited on hold for over an hour, and finally spoke with someone who claimed they were able to update our reservation. I assumed I would get an email noting the changes, but nothing ever came. However, when I then went to check in this morning XXXX before the flight, the reservation now only included details for me, my son and my daughter, and my wife was no longer included in our reservation. I called Southwest to see what happened, and they said they did not see my wife on the reservation. I then had to call Chase again to see what happened, and it was only then, after another XXXX on the call, that they shared with me that my wife was moved to a new reservation with a different confirmation number. Mind you, this was not displayed on the Chase XXXX portal when I logged in to my account, nor emailed to me after my long call with Chase the day prior. So, after they gave me the new confirmation number for my flight, I was able to check her in, but in a different group than the rest of our family. Needless to say, this whole experience was incredibly frustrating. So, I called Chase back yet again to express my frustration and ask that they submit my complaint and please have someone follow-up with me for some sort of resolution ( either refund points or funds ), but they said they would submit a compliant but that I would not hear anything back and that no recourse could be offered. For a credit card with a {$550.00} annual fee, to be overcharged on the cost of the flight and then to get the runaround with issues caused on their end, not mine, this is incredibly frustrating. I also think it is very poor form for Chase to actively promote their travel portal website when examples like this clearly show it is a ripoff and the fees magically are added after you select the priced out flights. This is not transparent and is also very frustrating. All of this is why I am submitting a complaint for CFPB to review. Note : Attached files show the email confirmation with names correct after purchase ; they show the difference in price between what I paid ( {$1200.00} ) and the price Southwest was charging at time of booking ( {$1200.00} ) ; and show how our names were transposed incorrectly when Chase moved the info from the travel portal to Southwest for the booking.