This is OP. I like PP's idea of a written positive reference and answering specific questions if prospective employers choose to get in touch with me.

As to why it didn't work out, I agree that personality clash is part of it and will definitely say this to any prospective employer. But it goes well beyond this. I realize now that someone as absent-minded and forgetful as she is doesn't realize there is anything wrong with them so likewise, why are they going to be sorry and take ownership when isn't it normal to forget things or make mistakes? Once, we scheduled weeks in advance for her to come in early and when I reminded her the week of, it turned out she had mistaken the time (not the first time) and made conflicting plans. Never said sorry or offered to cancel her plans or at least explain why she couldn't. The time she asked to leave early the day of, she had made the appointment THREE WEEKS PRIOR. Did not apologize or seem embarrassed at not telling me sooner, but actually implied I was to blame for not having a calendar she could write in... completely ignoring the fact she writes daily in a notebook which is for this purpose so yeah, my fault. Sorry for the rant (it felt good, though)!

Sounds like there is a communication break down and perhaps a personality match clash, both often responsible when the arrangement does not work out. If your nanny is good at her job then give her a fair reference. It is not unusual for nannies to lose their job because of communication issues but the attitude does not sound professional. It also sounds like your nanny has issues with time management, not all nannies are good at this but they should work at improving this skill if they want to be seen as a professional. Take this as a learning experience for both of you but you are right to let your nanny go but do be fair with her, you could only decide to verify that your nanny worked for you for X amount of years and that is all, this way you do not set yourself up for any anoying lawsuits.

Nanny here. PP handled it just right. Write all the positives you can think of and give her that and if they call answer questions honestly.
"Tell me about Larla."
"Larla cared for my child Larlo from age X to age Y about Z hours per week."
"What was it like working with her?"
"My kid felt ABC about Larla. I think she and I weren't a great match personality-wise, but many of our friends and neighbors told me that she took excellent care of Larlo when they were out together."
"In what way were you a bad match?"
"I felt that she wasn't proactive in scheduling time off and didn't always handle logistics well."

If they really want to know they will ask.

If someone fired me I wouldn't be using them as a reference.

Good to be very careful about putting anything negative in writing.

I went through this as well. We had several conversations before I fired her. And I wrote a reference stating all of her positive qualities and left out mention of anything else.
It was almost exactly the same issues. I think my previous nanny would be a really great nanny for someone who is looking for a companion for a small child, but doesn't really have a stressful job themselves and is able to take on all of the household tasks after work. She was almost like my 2 and 5 year olds' best friend. She took them out shopping, to playgrounds and museums and out to lunch, taught them all sorts of things, and they loved her. But she was unprofessional, lazy with picking up after herself and the kids, and generally made my life more difficult. Several people who got my reference letter called and asked specific questions about professionalism and housekeeping after noticing the holes in the letter. She is still looking for a job, and I hope she finds one that is a good fit for her. I think she is going to have to ask for considerably less money though.

Our nanny is great with DC, other mothers compliment her to me, but she has her issues. Biggest is her attitude and I am really fed up. She never takes responsibility for her mistakes, acts like it's the world's fault when she forgets that DC's appointment is at X time or forgets to ask me in advance when she needs to take work off early (and as a result, I say no). I expect to let her go sometime this year and do not know how to handle the parting and reference. I think the fair thing would be to tell her in nicest, constructive terms why I am letting her go, but I imagine she will ask me for a reference? With our last nanny, I was able to give her a glowing reference yet spoke honestly but in a positive manner when asked about her weak points. I do not feel like I can give this nanny a positive reference.