Professional Trouble

I try to like people. In general I can find something in people that is redemptive in my overall accessment. So what happens when someone you have had trouble finding that in, does something that sinks them further in the hole of your estimation? When you have to lead a person you don't respect, who does a crappy job, and who makes unfunny comments for everything, how do you maintain your patience and not let your disgust drip off you? I feel like a phony being nice to her, the job requires that I can't just ignore her, and I have a strong desire to be a good leader and a good person. I feel she doesn't respond to my leadership style and that I don't want to lead her. She is a weak link in the team, but not one I want to protect and nourish. And strangely enough for me, I don't care if she likes me either. But I do care about being professional.