No one else has raised the issue of your nanny and your housekeeping, so I will.
When the decision was made that nanny would become your cleaner ("She is responsible for doing the housekeeping (laundry, vaccuming, bathrooms etc.) while the girls are in school. "), was that YOUR choice, or HER choice?
I think many times nanny burnout happens when more and more cleaning duties are added to the list of expectations. And yes, I know she has 2 - 2.5 hours a day each school day to fill, but maybe her attitude is due to feeling less than valued for her childcare skills, and more prized for her cleaning abilities.
I would suggest you talk with nanny and see if you can determine what is causing her dissatisfaction. Then you can decide whether you like her enough to take steps to fix any issues that are causing her attitude to be poor, or whether between the strain on your budget that a higher pay rate will cause and your needs that she isn't happy about fulfilling, it's better to part ways.
If you do want to keep this nanny, and if the housekeeping is what is souring her performance, maybe she can add value to your lives in some other way. Grocery shopping, errand running, organizing, household management, cooking, etc are all possible chores she could take on instead of cleaning.
Good luck!