Thanks everyone for all the feedback! I've been on the Dis long enough to know not to ask a WWYD question if I didn't truly want honest opinions. If I was looking for everyone to agree with me, I never would have posted.
On the drive home, I really struggled with how I would handle it. In the end I thought about my own kids who were 16 not too long ago and what I would have wanted for them in that situation. If I knew my kids had three jobs scheduled, have been paid in full for the first job, but they suddenly weren't wanted for the other two jobs, I would wonder what the heck happened. I would at least hope that they knew exactly what happened even if they didn't share it with me. I am hoping she learned from it and I did learn from all of you. I appreciate the suggestions and the other ways to approach the situation. I do believe I was very calm, non threatening, and I was very brief and to the point. I'm wordier when I type compared to when I talk!
There is one thing I adamantly disagree with that a few people have brought up. Some have suggested that I might need to loosen the time constraints that I set. I went over the times with this girl on two different occasions (email and in person). I specifically told her to let me know if a certain time didn't work out so we could work on an alternative. She was scheduled to come over four different times. Of those, three times gave her a one hour window and the other time was "anytime before 8am." I spread the times out so my dogs wouldn't go too long without a bathroom break. Because she ignored the times, it is likely my dogs went 16 hours without going out and the other time they only went 2 hours and 45 minutes before going out again which was totally unnecessary. If she had a "real" job, they wouldn't give her the flexibility I provided and allow her to come in anytime between 5 and 6pm. She lives five houses away from me. This was hardly a hardship on her and if those one hour windows were too inconvenient for her, she never should have taken the job. As the "employer," I do get to set the times and the rules even if they are completely unreasonable (which I don't think they were). She has the opportunity to decline the job.
On a positive note, two of my favorite college kids are coming home just to cover my upcoming week long trip in a few weeks. They are splitting up the week. They have been dog sitters for me since both were 13. Yes, 13! The job is easy enough that a 13 y/o can do it. They will be rewarded very well for their time, I assure you. I have one last trip set up for December and then we are done traveling until probably this time next year. I think some of my college kids will be home already in December so I should be able to find someone. That will give me a year to work on finding some new people.
Thanks again for all the feedback. I really do appreciate it. While many of you gave me some things to think about, I am satisfied with the way that I handled it.