I work in a residential care home for learning disabled and mentally ill people. I agree with you about getting the right balance of firm but fair. The people I work with can be extremely volatile, if they don't like the way I have spoken to them or enforced a rule then I will be at risk of being verbally or more likely physically attacked.

They take advantage of the fact that I am new. They are very sensitive to my disposition and will exploit any sign of weakness.

While this is different to your work, it is similar in that you need to hold yourself with confidence all the time. Even if I feel like crap, I need to go in appearing to be perfectly well. I think of it as acting in a play. After an hour I start to actually feel the way I am acting.