Have you tried viewing the exercise, as a way to work some of the emotions of your daily work, out of your system, so it helps you to keep the things seperate to some extent?
Maybe that is what is needed, just to keep a positive spin on the workouts, and also to remind yourself, you're doing this for you, because if you didn't workout, you might increase the risk of getting a problem in the future, that people you treat may have.
Worst thing would be to work in a place like that, then by the age of 70, be in one.
Not trying to sound a like a profit of doom, but of course all the health benefits can't be overlooked. Plus you ARE worth a lot of the time and effort you give to yourself.
You deserve to be healthy, and deserve to have good quality of life, so it might not seem easy to do, but for your own future, and your own health, you owe it to yourself, and deserve to put the time in.
I know you can manage to do this, you just need to be strong, and be patient and understanding with yourself.