Time to seek advice as to your legal rights with the dealer.
:yeahthat:.
From what I've read, you've been sold a dud car with a worthless warranty.
As you've bought it recently, you have rights under the Consumer Rights Act 2015.
Unfortunately I suspect that enforcing those rights may prove to be as difficult as getting the car repaired properly; I doubt either will be straightforward.
Dualogic faults can be an absolute nightmare to diagnose and fix; franchised dealers generally approach this by replacing major components and the cost often runs into thousands of pounds. Whilst there are sometimes other repair alternatives, finding anyone capable of working out what is needed is not easy; most independent garages have neither the experience nor the capability of diagnosing and fixing dualogic issues.
I feel desperately sorry for you. You paid good money for the car and didn't expect this.
Personally I'd explore the possibility of enforcing your rights against the selling garage before you start messing with it. If you bought the car in England, then English law will apply - I don't know how different things are in Scotland, nor how easy it will be for you to find someone local who can advise you on this. However I do know that used car dealers know every trick in the book when it comes to avoiding their legal obligations; I doubt it will be straightforward.
I'm hesitating to post the link as I don't want to depress you further, but
this thread gives you some idea of the problems others have had with these transmissions.