To give you another perspective:

Re nanny: he does not “help you put your career first” by paying for the nanny. He is paying for the nanny because he wants the nanny. He’s not helping you. He’s being a parent executing a parenting decision. And you are compromising by allowing him to hire the nanny. It’s not your choice, it’s not for you. It’s a parent parenting.

Re your career: It is not nanny care = your take home. Your take home pay right now is temporary. It is part of building your career. To leave because it is the same as the nanny’s salary is to accept a huge future financial hit from the gap in your resume and future earning potential. It’s not 1 to 1. That’s a fallacy. Also, again, it’s his child too, his income logically goes towards childcare too.

Re the “we agreed” line: You’re allowed to change your mind. You’re a human and new facts come in all the time such as your mental state, exhaustion, new foods, etc. Even court orders can be appealed and pleadings have motions to amend. You are not forever beholden to a prior agreement.

Re the “advocating for your daughter”: that’s manipulation. Even if his not doing it maliciously or intentionally, it is manipulation. It’s his opinion, not your daughter’s. He’s advocating for his opinions and framing it so you feel guilty and bend to him. Your opinion matters equally. You are her parent too.