Complete ripp off

I'm extremely dissatisfied with Cheapoair as a service provider. At the airport I figured that last name was swapped with the first name for both my parents. A representative from JetBlue told me that she can fix names only for the first airline carrier, but we might stuck at another connection point with a different airline company. So, I was advised to call to cheapoair and ask them to swap names. The representative said that I had made this mistake which is not true and they wouldn't change anything for me. The interesting fact is that I bought tickets for parents 5 months ago and confirmation emails in both cases look exactly. So, that means I entered everything properly, and the only one reason why everything happened was a bug in the system. I pointed a representative to compare names on both confirmations and I was told that I made the same mistake first time too. How come my parents were able to fly with wrong names on tickets?! Instead of finding a solution, a representative started offering me extremely expensive tickets without giving me any credit from the current tickets. On my opinion, everything could be sorted out if that guy quickly called to airline companies and explained this situation. In the end he said that in order to get a possible refund I need to cancel both tickets knowing that my tickets are non refundable and pay 50$ each what I did. Of course, after I calmed down I called back and asked to refund all cancellation fees. I asked for a proof that I made this mistake because nowadays companies use tracking tools which record users' actions. He said he sees that on a screenshot and period. I called second time asking to present me proof and the second representative hung up on me. After that I talked to the third representative and finally with a supervisor who in 45 minutes from the beginning of the conversation just sent me a screenshot where names were swapped. I asked for a capture because it's easy to mock up this page but she said she was not technical enough to understand what I want. It's a complete rip off without any meaningful proof. Very poor customer service and its name really says what service you're going to get. Cheapoair completely ruined all my parents plans and in addition my mother had a nervous breakdown. My money loss is 1108$. :(