From the most feminist friendly translation, the NRSV Updated Edition, the text reads:
"To the woman he said, 'I will make your pangs in childbirth exceedingly great; in pain you shall bring forth children, yet your desire shall be for your husband, and he shall rule over you.'” (Gn 3:16 NRSVeu)
view a verse in the next chapter with a parallel phrase
"If you do well, will you not be accepted? And if you do not do well, sin is lurking at the door; its desire is for you, but you must master it.” (Gn 4:7 NRSVue)
There is not a marginal note giving an alternate translation in either verse in the NRSVue.
"Thy desire shall be to thy husband; thy desires shall be referred or submitted to thy husband’s will and pleasure to grant or deny them, as he sees fit. Which sense is confirmed from Gen 4:7, where the same phrase is used in the same sense. And this punishment was both very proper for her that committed so great an error, as the eating of the forbidden fruit was, in compliance with her own desire, without asking her husband’s advice or consent, as in all reason she should have done in so weighty and doubtful a matter; and very grievous to her, because women’s affections use to be vehement, and it is irksome to them to have them restrained or denied. Seeing, for want of thy husband’s rule and conduct, thou wast seduced by the serpent, and didst abuse that power I gave thee together with thy husband to draw him to sin, thou shalt now be brought down to a lower degree, for he shall rule thee; not with that sweet and gentle hand which he formerly used, as a guide and counsellor only, but by a higher and harder hand, as a lord and governor, to whom I have now given a greater power and authority over thee than he had before, (which through thy pride and corruption will be far more uneasy unto thee than his former empire was), and who will usurp a further power than I have given him, and will, by my permission, for thy punishment, rule thee many times with rigour, tyranny, and cruelty, which thou wilt groan under, but shalt not be able to deliver thyself from it. See 1Co 14:34; 1Ti 2:11-12; 1Pe 3:6." Matthew Poole (1624-1679)
"Women should be silent in the churches. For they are not permitted to speak but should be subordinate, as the law also says." (1 Cor. 14:34 NRSVue)
"Let a woman learn in silence with full submission. I do not permit a woman[c] to teach or to have authority over a man;[d] she is to keep silent. For Adam was formed first, then Eve, and Adam was not deceived, but the woman was deceived and became a transgressor." (1 Tim. 2:11-14 NRSVue)
b - or wife; d- or her husband
Man was created "good" or righteous, not merely innocent. Therefore his rule would have been good and righteous and not abusive as happens in the fallen state of man.
"Thus Sarah obeyed Abraham and called him lord. You have become her daughters as long as you do what is good and never let fears alarm you. Husbands, in the same way, show consideration for your wives in your life together, paying honor to the woman—though the weaker vessel,[a] they are joint heirs of the gracious gift of life—so that nothing may hinder your prayers." (1 Pet. 3:6-7 NRSVue)
a- or body
The scriptures, which are God's word (2 Pet. 1:20-21), are very clear on the question.