Hope you feel better!! If I were you, I would take the days off and try not to this family make you feel bad or guilty about it. They have signed the contract and if they don't want to abide by it, they are free to leave. We all have choices and if they choose to stay than they are also choosing to follow your rules.
I don't like to take sick days either but pneumonia is serious and I would feel awful if I passed it on to the children regardless of who I got it from. Rest up and take it easy!!