I was a nanny for 15 years.
Likely scenario: she is taking your baby to her home whilst she does her housework or watches Jeremy Kyle (am making huge assumptions here but lets just assume she's not watching tapes of Newsnight and Question Time )
She's not making the lists/keeping on top of your household stuff because she's never in your house. Does she get on ok with the au pair - is there a jostle for who's in charge of whom?
She doesn't answer her mobile because she doesn't want background noise to give away where she is, or feels like you're checking up on her because you don't trust her (like, duh.)
Get rid. You will find another nanny who will love your baby so much she will actually take good care of him.
For what it's worth, your job sounds like a good one: I had 5 kids (from 2 families), 2 at full time school, one at nursery and two at home at one point without an au pair and I was NOT supernanny.
The Lady. It's out now in all good newsagents. A shit read, frankly, but get an ad in pdq.