It sounds like your nanny previously cared for your first child when you worked outside of the home. Now with you being home ten hrs. a day, the dynamic has changed dramatically, not in her favor.
I am sure you are truly concerned about their whereabouts during the day as any normal mother would and should be.
However, please keep in mind that for many nannies, working alongside the parent in the home is very complicated. It's like working in an office where your boss is right behind you, watching and listening to everything that you do.
Not saying that is what you are doing, but that is the gist of it.
If you want this whole set-up to work out and you most definitely DO NOT want to lose your nanny, then I suggest you back off a little, choose your battles wisely and give your nanny complete autonomy in her job.
Concentrate fully on your new baby and take some of your focus away from your nanny and your DD while she is in charge.
There needs to exist an important level of trust here and if you are texting her during the day, that might be a sign that you do not trust her completely. And if the nanny gets wind of this, she will understandably feel uncomfortable around you.
Good luck.