Squiffy's advice is excellent.
As a general guide references must not give a misleading overall impression, and must be based on facts that can be substantiated.
In other words, if it is very clear that you raised these issues with your nanny and ideally made notes of the conversations and she still didn't pull her socks up, it's fair to bear that in mind when giving the reference.
If you didn't raise issues or give her the opportunity to address your concerns, it's not fair to use them in a reference, and in any case she could challenge statements like that. The issue about insisting on time off, for example, she could quite rightly challenge that saying you could have said no, which you could, however bad you might have felt about it.
Normally I'd recommend a facts-based reference only where an employer doesn't feel able to give a glowing one, but, as Squiffy points out, that's really not an option here.
Think very carefully about the options Squiffy has mentioned. The impact of a poor or limited reference on a nanny as opposed to a 'normal' office worker could be huge and career-limiting. If you feel strongly enough to feel that's fair, and feel that the issues were that important and well-documented, then fine.
I would agree with Squiffy's option of 'forgetting' bad stuff not mentioned and give a positive reference on good points. It sounds as though this nanny isn't bad enough to have her career damaged, and just needs someone to take a firm hand. You shouldn't give a misleading overall impression to the potential employer as I've said, but in this situation it's very difficult and if you haven't addressed any issues firmly and officially, you must bear some responsibility.
She may well not have any of these performance concerns at a future employer. It sounds as though there is a little bit of her taking advantage of you and you perhaps being a weeny bit 'soft'? She obviously felt as though she could manipulate you, and with a new employer she may not feel that, or they may squish such an attitude sharpish, in which case those issues aren't actually as great as they feel to you at the moment.