I used to be a trainer, or a teacher, of people and their dogs. I’d see them once a week then send them off to do their thing, only to discuss what they could improve upon the next time I saw them. Sometimes I’d only see a person once. This is still how most trainers operate–that’s the nature of working with people and their pets.
But in agility most trainers work with their clients over months or years; and while they might only see them once a week for classes or lessons they also see their clients on the playing field. This can produce some interesting dynamics; and it is in everyone’s best interest to draw some clean boundaries. 
An agility trainer will burn out fast if she isn’t clear with her clients about if and when they should approach her for help at trials. Similarly, clients become dissatisfied if they believe they are owed one service but receive another. What has worked for me here isn’t what will work for everyone, but I think it’s worth discussing.
When I was an agility trainer I saw my students once or twice a week, and was always excited to see them competing on the weekends. On those weekends I was clear with them that I was unavailable anytime I had a dog with me or when I was wearing headphones. Other times they could ask me if I had time to answer a question, watch their run, etc. and I obliged whenever possible. Without these rules there could be misunderstandings or hard feelings, and it worked out well for both my students and myself. While it is nice of a trainer to hang around until novice to watch her students run their young dogs; it’s not part of the service these students are paying for if they just attend a class or lesson weekly, and it’s important for everyone to take note of that.
My work is now online with weekend seminars once or twice a month. With my current private clientele I am much more of a coach than I used to be. For me, the difference lies in responsibility. If I am someone’s agility trainer my job is to help them be better at agility and that usually entails foundation training, advanced skill training, and handling help. Now, in private coaching, my work is holistic. What my clients’ dogs eat, how they sleep, what kind of exercise they get, and how they are communicated with at home are just as important as their start line criteria and handling system. I need to know it all, and I advise on it all. If my client is having a meltdown about her dog’s behavior I need to be as available as possible to help her through it. I am not around 24/7 as I can’t be, but I do think on and care about the entirety of the situation when it comes to my clients and their dogs.
So what’s the right way to do this profession? There isn’t an answer to this. What will be best for one client won’t work for another (plenty of people have no interest in adjusting their lifestyle in order to achieve better performances, while others feel cheated if they don’t receive all the information I have). What kind of professional we all want to be varies too–I am much less likely to run into clients at weekend trials or big events now, and that suits me well as I can totally focus on my own dogs. While I am more available to my clients on one hand, I am also better able to compartmentalize and run my own dogs when I don’t have clients that need help analyzing courses. 
Whether you need a coach or a teacher might also have to do with the problems you are facing. Serious behavioral concerns warrant coaching while sloppy front crosses or missed weave entries might just require training. It would serve us all to think a little harder about what we want in our professionals, and about what sort of professional we aim to be.
