I am also a nanny who works with multiple families. I always keep a hat, and two full changes of clothes in my bag. I also own stock in purell.
On a day-to-day basis, you just have to assume that you have already been exposed. At that point it doesn't really make sense to worry about avoiding further exposure, as most likely they were with you during a time when they were more contagious than they are once they get actively sick.
That said, I would have quit if a family failed to notify me that their children have lice. That is completely an acceptable. That is something that you could easily have avoided catching (by wearing a scarf over your hair after already spraying your hair with essential oils), so the only reason you were exposed was because they did not tell you. That is totally not okay in my book and I absolutely would not have worked for that family again.