This is perfectly normal, so don't get so worked up over it. It's natural to feel like someone is crossing into your space... but remember, that's why she is there - to help you recuperate and look after your baby.
Also remember she is a temporary inclusion in your family.
I know how frustrating it can be for you, but at least you know that your baby is truly happy with your nanny and that when you are gone he/she is in good hands.
Don't see your nanny as a rival, but as an extention of you.