Has having Murphy done eased the situation or is he still being jealous towards your older dog?
If so then always praise them separately as said before and always the dominant dog first... we as humans automatically go for the weaker one, our reasoning is we do not support bullying, but in the animal kingdom it don't work like that lol. Your older dog seems happy to be submissive and let Murphy be more dominent...... but .... if it is a case that Murphy is just freight training your other dog all the time then that is different.
As for you vet OMG
This is why you need to vet your vet, so to speak and go by recommendation if able and I would suggest changing to another vet OR do several visit to your vets for meets with the nurses and the vet again for nothing more than overcoming his apprehension.
We make the problem worse as we only take out animals to the vets when they are ill or need something done and we should take them for random things like once overs with the nurse just to be weighed is a good one and gives our pets good experience and non association with it being for bad things only.
Pets at Home many have their own vet clinics and have scales and the reception/nurses are fab if you explain you are just helping a dog over coming their fears.
I do this a lot when I have nervous and fear aggressive dogs to foster etc these are what I specialise more so in ... for my sins lol
Also always worth being registered with 2 vets and also enquiring when their next open day is as good to see behind the scenes.
Always get your dogs crate trained helps if they ever have to stay at the vets.
Debbie x