I always have my phone on me while working my current position. I communicate with my MB throughout the day and when the children are napping, I am reading the news or playing around on dcurbanmom

When the children are awake, my phone is on my person but I am not texting or making phone calls. I've interviewed for positions in the past where I was asked to keep my phone in my purse all day. Not an option. In addition to nannying, I'm a caretaker to my FIL and need to be able to have access to a phone in case of emergencies.
Have a talk with your nanny. Let her know that you expect her to be engaging with your children and not on her phone all day. A simple text or two shouldn't be an issue but to be glued to the phone is unprofessional and unfair to your children who have obviously noticed they aren't getting the attention they deserve. Why are you paying for her cell phone? Is she a live-in? I think if she knew you were looking at her phone records she would be mortified.