Anxitane is the brand name of the supplement the trainer is referring to. L Theanine is the active ingredient. It is in blends of other supplements as well at lower levels than in the Anxitane. Anxitane is my preferred product and I have seen it help facilitate behavior modification.
Desensitization and counterconditioning of dogs with profound anxiety is a process whereby attention to detail and keeping the dog below threshold is important. I know as I own such a dog. I don’t like to ever see reactive dogs on neck collars. Initially I used a head collar and/or front attachment harness. The most frequent mistake made is putting the dog in situations that he/she is not ready for. This takes time… a lot of time and realistic goals.
General obedience classes may be inappropriate for your dog as many dogs are over threshold, Feisty Fido classes where the ratio of trainer to student is often one to one and they use screening between dogs to keep them under threshold until they are ready for contact can be helpful
You might want to buy Patricia McConnells book Feitsy Fido which is an excellent resource. If you are not familiar with BAT it is a useful technique https://www.youtube.com/watch?v=5WrseJPY09k
Working with a board certified vet behaviorist, a CAAB or a vet interested in behavior would be an excellent idea check here http://avsabonline.org/resources/find-consult
or hook up with a Karen Pryor trainer which you can find here: https://www.karenpryoracademy.com/find-a-trainer?source=kpctnavbar
