The wording was clearer previously, but it is known that EY and EK will not drive a pax between AUH and DXB and vice versa. Staff are also trained on this so I'm not sure how even if it was input 1) it was confirmed and 2) agents said it was fine. EY call centres may not be great but they definitely know this rule.
By all means, lawyer up over a few hundred dollars but I think you'll find that you won't win.
The T&Cs aren't clear and, to be honest, this is the first I've heard of the carriers not transporting people between the two airports. I've taken plenty of trips between Dubai and Abu Dhabi using EY and EK driver services and never had a problem. Admittedly, only about 4 have been from airport to airport but the conditions are certainly not clear if they wish to exclude that.
Regardless, the OP should have had no problem organising transport from AUH to Dubai itself which would have saved a lot of money.
I still believe a credit card chargeback is a good option.