I have watched the vet clean teeth and is pretty simple with a pair of hemostats.just put them on the tooth almost half way around tooth with handles down and press and squeeze at same time. The plaque wit break off and leave tooth clean. Repeat until tooth clean. That's it!That is bull. Vets should be doing full cleanings when needed. Some dogs/cats have genetically very bad teeth (not yours! just an example) and if you waited until they were five the teeth would be decaying out of their heads.
I happen to have a cat like this, and don't want to risk anesthesia, so I found a vet dentist tech that does non-anesthesia dental cleanings and have her do both of my cats every 6mos. It keeps up with the tartar build up and I shouldn't ever have to put them under anesthesia just for a cleaning.
Anywho, what I was getting around to is that the yellow is plaque, which is about impossible to remove without a scraping once it's hardened. The gum will stay irritated and red until it's removed. On the plus side, it doesn't sound near bad enough to require a full cleaning (likely why your vet refused - big risk w/ anesthesia, little reward). You might be able to find someone near you who will do a non-anesthetic cleaning like I have and that will take care of it and allow the gum to heal. Or, there are sprays that advertise that they dissolve plaque and you could try one of them. Be aware that I've used one and it didn't seem to help my cat any. I found them to be expensive, too.