I agree with all of the above statements, but as angry as I would feel, I think someone needs to act like the adult in this situation. Confront your husband first, give him a chance to explain. Is there a chance you might be misconstruing something? If you really love your husband, and would like you marriage to work, this would be the best place to start. Fire the nanny, but not before you have a new one lined up. Consistency for the kids is the most important thing, especially if you think this will end in a divorce. Follow up by filing a complaint with the service through which she was hired. Her behavior was not only morally wrong, it's unprofessional, and her superiors should be made aware of it. First and foremost, try to shield your children from this as much as you can. When they are older they will make their own opinions about this situation, and if you conduct yourself as you would truly like to, explosively, your children will blame you as much as your husband, and they deserve a safe place/ person that they can count on.
This is a very tough situation, and I'm truly sorry if this is more than a hypothetical question for you. Just remember no one deserves to be treated that way, and you deserve better.