First, this is not a straightforward situation and nobody, not even an animal behaviourist, can diagnose or even assess this situation from these posts on a forum.
There is a very significant confounding factor of an anxiety disorder-type history in the 1.5yo dog which has a huge influence (if not the sole influence) in this situation.
Unfortunately you're at that middle ground where turning to a behaviourist is not quite sufficient - you may be that owner that needs to look at pharmacological support for the anxious dog. This does NOT replace training or behaviour modification. It is not "drugging the dog into stupidity". The same way if you have diabetes, insulin fixes that physiological imbalance - these drugs are designed to fix neurotransmitter imbalances. They assist a dog that cannot control their anxiety like most dogs, so it is not a crutch to use them but you could make the argument of how humane is it to not give the dog access to a drug that will alleviate the anxiety they're living with.
You're also not at the right spot just going to a vet. I don't believe trainers should be dispensing veterinary advice nor veterinarians acting as behaviourists (I've taken the same course that the vet students get at the vet college here, doing a BSc). Even Karen Overall has been outspoken about the fact that she hears as much misinformation on training & behaviour from vets as she does from the dog owning public at large. A lot of vets are still very behind the times and focus on pack theory (largely disproven as it was used in training for years) and "dominance". A vet is who you should be consulting with the older dog, but you really need a behaviourist.
If the older dog is stressed, you could run into continued problems if you force him to be around the trigger (if that's the puppy). Do make sure if he shows you signs he's anxious, you allow him retreat. You will make the anxiety worse and really exacorbate the problem by allowing him to create a negative association with the puppy. You need to be focusing on classical conditioning right now, not operant methods.