2004 Jaguar X-Type Can I claim my money back?

Recently my car was towed by the AA to Charles Hurst Jaguar Garage in Belfast as the AA mechanic could not resolve the issue of major coolant loss. The level of cover I have is keep mobile and repair costs paid for by the AA. The car sat with the Jaguar garage for two days. They carried out tests, Topped up the coolant with only water and couldnt find the problem even after telling them that the loss of coolant was during motorway driving. I had to pay jaguar £191 to release my car for the testing they carried out. The following day again after motorway driving a complete loss of coolant. The AA were called again. They tested the car and then charged me £11.99 for a bottle of K-Seal. This has resolved the problem of coolant loss. The second AA mechanic solved the problem where the other didnt and neither did the jaguar expert mechanics. Am I entitled to a refund from jaguar or from the AA due to negligence on the first inspection jumping to the conclusion that this problem could not be resolved by the roadside? Grateful for a response. Thanks guys