From what you have said, they are trying it on. If a service interval runs over by 2000 miles, it doesn’t suddenly cause the vehicle to break. Certainly not with an oil change.
It might have made a difference if it went over by 20,000 miles but not by 2000.
However even if that first service had not been done the fact remains that the vehicle was running fine before they did the current job and now it is not. If they knew it would cause a problem doing the later service oil change because the first one was late (I do not accept that at all) then they shouldn’t have carried out the second one and should have advised you so. They should have also advise you of the potential problems.
I will admit that I do find it extremely strange that all they did on this latter occasion is change the oil and yet after the oil change there is a fault. Usually, it’s the other way round and certainly with an automatic gearbox, it will run better after the oil change than before.
At this stage of course they are simply unwilling to do anything or accept any liability other than supply you with a new gearbox. If they simply refuse to do anything else then your only alternative is to take them to court.
As you appreciate, taking this to court could take some time and matters like this routinely don’t get to court for upwards of 12 months. For that reason, and because you are also under a duty to mitigate your loss, the suggested remedy here would be to replace the gearbox or do whatever needs to be done and then to seek the cost of doing that through the courts if the dealer will not pay up.
In my experience, dealers routinely replace units (including a whole gearbox) which could be repaired much cheaper. For that reason, you might want to visit a separate independent gearbox specialist to get an opinion as to whether it does need complete replacement or whether it is repairable and if so the cost.
What you are also going to need is the opinion of an independent specialist to confirm what the problem is and what caused it. This latter point is most important because without independent evidence as to what caused the problem and that the problem was caused by the dealer, then you have no claim to make.
I fully understand that there was nothing wrong with the car when it went in but there is a problem when it came out. Although it seems unlikely, that could be coincidence and that something was on its way out anyway. Sometimes, you drive your car and then stop it and for some reason it won’t start. It’s not necessarily the fault of the car park the car won’t start. The situation that you are in May be the same with regard to the dealer. Only when you get the expert evidence to find out exactly what has caused the problem, will you know whether the dealer is at fault or not and only then will you know whether it’s worthwhile taking the dealer to court or not if the dealer will pay up.
Once you have that evidence and you present it to the dealer, you may find them more willing to deal with this.
Can I clarify anything for you?