And while training is challenging, I find that teaching is more so - the students are depending on me, I need to plan the classes, and stay fully focussed while I'm there. It can be quite draining after already putting in a full day's work. Some days, I really struggle to get to the dojo, knowing that I'll most likely have to teach.
Interestingly, I think the issue is not "teaching" per se but the way you have contrasted "teaching" and "training". For instance, "the students are depending on me". Well, when you are training, every partner you have is depending on you. I know that often folks don't think of it that way, but it is true.
"...the need to stay fully focused while I'm there." It shouldn't matter one iota whether you are teaching or just training. If your training is conducted properly, you should be fully focused every second you are training.
Many folks treat their training as recreational. This contrasts with other situations in which what they do is more "serious". For instance taking ukemi from the teacher, taking a rank test, doing a public demo or teaching classes to others.
There really shouldn't be a disconnect between what you do on the mat in class and what happens in any other aspect of your training. If folks trained in every class the way they treat what they do on a Dan test, they would progress at a far greater pace.
If you feel that having to be "fully focused" while your teaching makes you more tired than regular training, you aren't focusing properly in your training. Training is about
being fully focused.