Eh you're kind of correct. 'woman' is not the subject in either interpretation. She uses 'like a woman' as a simile to describe the rest of the line. The subject will always be 'me' and the object will always be 'you' because she is doing the action, while he is being affected by the action. This also applies for 'like a baby'. You are actually arguing whether 'me', or 'you' is being described by the simile 'like a baby'. Although they're both technically grammatically correct, I personally think it makes more sense for her lover to be the 'baby'.
This song is different from her earlier music because she compares herself to a woman. Before, she usually called herself a girl. She tells her lover here that she wants to love him like she is an adult. I don't think she would try and compare herself to a grown woman and a baby within two lines. In my opinion she's trying to sound maternal and caring. Also, it kind of makes more sense because you hold and care for a baby. Babies don't really hold people lol.
Idk maybe I'm wrong. I think you're reaching a bit though. Either way it's a cute line so idc.