I would ask all your friends who have nannies, that is how I found mine.
I would also not keep her, but in the meantime, I would ask why after you asked her to stay late that she said to your husband she had no idea. Also, did you give her a raise for the second child? Maybe she is not happy with her pay? It wouldn't hurt to ask her if she is happy because maybe it can be resolved.
And ask your husband to work with you. Make sure you both are telling her the same thing. It can be tough when you are dealing with a nanny because they are taking care of your children, but at the same time they are an employee. It can be a fine line, you want them to be happy but they need to follow the instructions you give. My nanny and I work as a team and we talk about the kids are doing, what they should be doing etc. That give the nanny input but for major things, I call the shots.
Good luck