I'm so sorry that you're feeling so low and demoralized
. I'm on my own most of the time because OH works long term contracts abroad so I really understand how much more difficult it is to cope with a challenging dog when you're on your own and have no respite.
My first thoughts on Archie were his age, diet, exercise and stimulation.
Age - Archie is a teenager and likely to be more challenging now than when he was younger.
Diet - What is Archie fed? Diet can have a huge impact on behaviour.
Exercise - Is Archie getting the right amount of exercise? Are you able to take him for a walk including off lead time before you start teaching your students? I try to make my walks a mix of relaxation (can be just sniffing and pottering around, meeting other dogs, trotting or running about freely) mixed in with a bit of focussed time doing some training and maybe some games. The training and games help them to focus on me. The rest of it is relaxation time for them simply to be dogs and chill or run or sniff.
Stimulation - If Archie is getting very hyped up each time a student arrives at the house he might be overstimulated and on a permanent adrenalin high during your working hours. I don't know how many students you have each day, but I wonder if his inability to cope with visitors to the house is either the root of his anxieties or a big factor in them? I have something similar with my 2 year old Cocker, Louis. At the moment I shut him in the study when visitors arrive and that seems to calm him down and make him feel more secure. That obviously doesn't work with Archie at the moment though and I don't know what else to suggest.
I know other posters have suggested that Archie might need more exercise and stimulation, but I wonder if he needs to learn how to focus and then how to switch off and relax. He sounds like a dog who hasn't found his off switch yet, bless him.
I wonder if finding a good behaviourist and having some one to ones would be your best way forward? I had to pull Louis out of training classes because he was so disruptive (noisy, reactive, unable to focus). I tried again a couple of times when he was a bit older I but had to stop again because he couldn't cope and neither could I because I felt such a failure. Your experiences with Archie at training classes sound so much like mine with Louis that I'm worrying that you and Archie will find it difficult to work in a class at the moment. Please don't think that's a criticism from me, it's a genuine concern. Maybe you could have a one to one with the trainer before you start the new class?