it is because of the strange smells that were on the cat from the vet  not
the vaccination.  I am sorry your vet is an idiot if he/she did not know
this.
if it was the vaccine the cat that received it would have been doing that
attacking

what you do is keep them apart when they first come back

take a dirty shirt with either your smell on it  or  take the shirt and rub
it all over the cat that stayed home then rub it over the cat that came from
the vet

you can also check to see about the low cost spray and vaccine mobile
clinics   they will do house calls for a nominal charge