i am not sure what your religion is but we solved this problem on a spiritual level. when it is bed time we take my daughter to her room and first read her a story and then from the Bible. we then say our night time prayers and leave her Bible open on her bedside table. i explain to her that the holy spirit from the Bible will always protect her and Jesus is always with us anyway. for some reason this works quite well as she says that she likes sleeping with Jesus watching over her - hope it helps

Clearly the big problem is that your daughter has not gotten used to being alone when she has to go to sleep. I also wonder how the nanny feels about having no time away from the child even at night. Is there no other space like a living room where you can make a small corner for your daughter to sleep all through the week and weekend? Then at least she won't have to adapt when the weekend comes.