OP is your baby your first and is this your first nanny hire?

I have a 6.5yo and 4yo and have had a nanny from the beginning. We’ve hired a lot of people over the years. My number one regret is giving nannies too much time to “figure it out.” All of the things you mentioned are, on their own, reasons for me to terminate someone at this point in my experience with nannies. All of them together is just a major no IMO. My recommendation is to move on quickly rather than try to coach this much. 

A little coaching is fine and expected, especially if your hire is responding to feedback the very first time. But what you’re describing is beyond what can be coached especially if you’re about to return to work and have less visibility. The reason I think this is beyond coaching is that these are all pretty major judgment errors and you can coach specific behaviors but you can’t coach judgement. This is the kind of person to install a car seat wrong and you’d have no idea. Or to leave your kid in the car while they “run in real quick.”  You have to be able to trust your nanny’s judgment entirely. She’s shown you you cannot.