Eh, I'll be real frank here: if you're not good enough to write something on your dayplanner (ok, dating myself there---if you can't put something in your online calendar or whatever), then you aren't responsible enough for ME to be happy with you watching MY kids. That's just plain and simple. Sounds like she's an average 20 year old who will do what she "has to" but will look for any short cuts she can. She may be "over" the babysitting thing (I was over it by 17, until after I became a mom again, lol). I am not dissing her, I was that way until I was about 22 (only because I had to then, as a youth pastor responsible for a lot of things suddenly), and I'm super responsible and a little anal about time management and my calendar now. Keeping in mind that her mother is your friend: I would do exactly this, because as long as you keep your tone in a professional manner (because you ARE hiring her, she IS working for you, afterall), just copy/paste both responses she gave regarding babysitting and email it to her with a note saying that you've had to find someone else to watch the children even though the plans were set previously, and that is unfortunate, but you hope that this won't be a situation that becomes common because you strive to plan ahead. Short and simple. You haven't burned a bridge if you needed her in a pinch, her mother doesn't have to get involved because she's an adult and you didn't get silly or preachy, just pointing out that she failed 2 times in a row to stick with the program. You don't have to "preach" to her, but by pointing out that it is her mistake like that is doing her a favor for when she gets a "real" job or takes on other sitting jobs. In the meantime, seriously look for another babysitter to take her place. Then you don't really have to contact or talk to her about it at all (if she's not a daily child care provider, but rather an occasional sitter, you just don't have to call her back for another job again). If she or her mother ask you about it, you can calmly say "Well, we found someone with more availability".
When we first moved here, didn't know anyone, but desperately needed a date night (months on end, very stressful situation, we needed some time to reconnect), my husband's coworker suggested her younger sister. I called and left 2 messages, and didn't get a callback, so she was off the list of possibilities. Another time, we wanted to go have a "grown up dinner" and were kind of desperate. The coworker mentioned she might be able to do it, so I called closer to the date and she was sick (missed work too)....I said Oh, Ok....and she said "How about my sister?" and I said nicely, "No, but thank you. I tried to get her another time and she wouldn't return my calls, so we'll figure something else out." She mentioned it to my husband, who simply said "No thanks". And it's never been brought up again, and it didn't hurt his working relationship with the coworker. It's just life. We need competent, mature, responsible people to watch our children, and we need to feel comfortable and confident that they will be safe and happy with their sitter, and the first sign of that would be whether we can feel comfortable and confident that the sitter gets the the stupid date/time right. We got a great sitter from a friend in my mops club (she passed me the number for her sitter), and are happy with her.