OP Maybe you should work on the sleep training on the weekend so the Nanny can continue what you started rather than expecting a new Nanny on her first day solo to start something the baby is not used to when she is not used to the new caregiver either. You are not being fair to the Nanny or your baby.
Sleep training shouldnt take very long, 2 or 3 days. So you work on it this weekend and get the baby where he needs to be.

OP here. Thank you for all of your constructive comments. I really appreciated them. I spoke to her about it that day, and I tried to be as clear as possible about what we wanted for napping and sleep training (the baby sleep easily at night, we're just working on naps now). After several attempts, it's become clear that she just doesn't want to deal with sleep training and the bottom line is that we just have incompatible styles, which is fine. To each their own. Thanks again! This community is great.

I am a nanny and I hav to say if this nanny agreed to work for you she should b able to follow and handle your instructions. About opening the blinds before picking the baby, she probably didn't want to trip over toys or furnitures in a dark room? Also if you are not kind to your nanny she probably won't do the job with her heart so I hope you repair your relationship over wise let her go.

Oh geeze another troll MB... You fire a nanny because she doesn't listen to your direction? You cannot always plan everything 100% with kids, things change, sometimes you realize other things work better geeze. My MB has a hard time putting her kids to sleep, when I do it for her, we read a book, play around the bed for a couple min, then they lay down and "see ya"
While mother stays in there holding their hands and stuff. No, but thanks. I'm a super experienced nanny, kids love me, but I will not do certain things. That compromise comes with hiring a nanny. Not every nanny will do things 100% the way you want it, that's called micromanaging and yes, you will go through tons of nannies and your kid will end up confused and developmentally delayed. Trolls.

I'm an MB (and admittedly a pretty critical one), and I think it is perfectly okay to open the blinds, etc. before picking up the baby. How I would deal with that situation as a mother, and how our nanny would, is to say some comforting words to baby before/as I am opening the blinds, that is the loving thing to do. Maybe your nanny did as well and you couldn't detect it on the nanny cam?

It would bother me if I saw a nanny did not do checks during sleep training per my instructions, assuming they were very clear, and that she was argumentative about it. But having said that, I think it warrants a discussion before you up and fire her. I've tried out several caregivers and what I noticed is that sometimes, no matter how clear you are, sometimes the person misunderstands anyway, or maybe they tuned out when you were explaining and don't want to admit it. Since she is so new, I would give her more time to see if these issues are one-time only, or a pattern.

I actually was in a similar situation earlier this year. I hired a new babysitter and gave clear instructions on her nap routine and that no CIO should be used. The second day, I came home early to find the sitter had left the baby to CIO in her room. I didn't fire her right away, but eventually, I did because from our talk, I got the impression that she knew what she was doing, i.e., not complying with my instructions, and didn't think doing so or CIO were a big deal. We clearly were mismatched in our care taking values so I had to let her go. If you conclude after talking with nanny that she understood your instructions, but chose not to follow them, I would let her go immediately. You do not want the headache of someone who will constantly disrespect your authority.

OP:
Nanny cams are solely for the purpose of detecting child abuse/neglect on video.

Not to sit around & micromanage someone every single second and nitpick everything that does not sit well w/you.

Plus how do you find so much time in your work day to spend so much time scrutinizing your nanny?
No offense, but you don't seem like you work very hard so it might be beneficial for you to stay home with your baby instead so you can not only cut the hourly expense of your nanny, but also do the sleep-training the way you prefer.

One final word....It is not a huge deal if a baby cries. Trust me it won't be the end of the world.

It would be a huge deal if you had a baby who actually never cried.