anxious dog, won't go outside, first day sitting. What to do to calm her/make her trust me more?

I'm watching two little fur babies over the next week or so, and met them 2 days prior to the initial sitting start date to get comfortable with them and more importantly, them with me. One has no problem with strangers; loves them and had no problem with me getting him on the leash. The other, his sister, well...she would come then run away when she saw the clip. She loves walks normally, and I know she's just scared now that her mom isn't there. I'm watching them and staying with them in their home, but wondered if any other sitters have dealt with a similar issue, and if so, how did you handle it? Thanks!