Product: Credit card

I have American Express ( Amex ) as a corporate card for work to cover travel and travel related expenses plus printing expenses. We also use American Express Travel Services. 
Our Amex expenses populate to a dashboard that we employees use. All charges populate except cash advances that I never use anyway. As employees we are required to code all of our expenses with specific codes for different customers. 
I had a complicated travel event last year with cancellations and ticket exchanges. When all of the charges came in I called Amex for clarification so I could code the line items correctly. There was some ambiguity and XXXX customer service rep insisted on putting a dispute on XXXX of the airline charges even though I made it clear I was not disputing, just trying to identify the charge. Subsequently I did identify the charge and submitted it for payment. Amex accepted this payment, and then later charged the same amount again when they removed their charge dispute from the account. I did not see this because, not having travelled in months I did not check statements or the dashboard because no new charges had been made. 
Then in XXXX they emailed me and said my account was delinquent {$920.00}, and they insisted on a XXXX payment of the same amount. After having to raise this with my manager it was submitted again. Actually paid for twice. I could not get any clarity on this and no XXXX on my employer 's side wanted to deal with it. 
This month the same thing happened again. This time in the amount of {$440.00}. This was associated with another disputed ticket. This had also been paid in full. In this case I was certain I had asked them not to dispute the charge. Again they were paid a second time for the same charge by my employer against my protests. 
To date they have double charged my employer twice and now they are charging me a late fee. 
Talking to them on the phone, they sometimes admit that they double charged me. Sometimes they deny it and say that its payment for crediting the account. This makes no sense because paying in full each time would zero out any credit. I have found the payment for the flight that my employer made and the XXXX billing in my Amex statements but they are unwilling to look at the evidence, will not provide an email address, and talk in circles. I explain the XXXX charging and they ask me to explain it over and over again. 
Their accounting treatment of this is not clear, and runs counter to a basic understanding of arithmetic. They insist that I reconcile the account. The dates and descriptions of their charges in their statements do not match the dates that they populate to my company 's portal for expense processing. This makes identification of the exact line items next to impossible. Then when I have identified the actual lines where they made the mistake ( reconciliation ) they refuse to look at it. This incident has cost me over XXXX hours dealing with them and my company, has been arbitrary, embarrassing and humiliating, and has disturbing to my peace and interferes with my ability to do my job. After all of this they are charging me a late fee. And this seems to be triggered anytime a charge is disputed, and this can happen with or without the card holder 's approval. 
I think they should have to wave the late fee at least, should probably reimburse my employer, and I think they should be investigated for a pattern of abusive behavior.