Matthew Henry agrees with this position, but he also adds an important point about the response of wives to this subjection. He states, “The whole [female] sex, which by creation was equal with man, is, for sin, made inferior, and forbidden to usurp authority, 1 Tim. 2:11, 12. The wife particularly is hereby put under the dominion of her husband, and is not sui juris—at her own disposal, of which see an instance in that law, Num. 30:6-8, where the husband is empowered, if he please, to disannul the vows made by the wife…Those wives who not only despise and disobey their husbands, but domineer over them, do not consider that they not only violate a divine law, but thwart a divine sentence [emphasis in original].” Henry hints at the fact that while the desires of a woman are subjected to the authority of her husband in the bonds of marriage, the desire itself is not necessarily to subject herself but rather to attempt to rule over her husband. This seems reasonable as the Scripture reiterates that in spite of this desire, the husband will rule over his wife.
This brings us to the comments of John MacArthur. Regarding the desire of woman, MacArthur has this to say: “Sin has turned the harmonious system of God-ordained roles into distasteful struggles of self-will. Lifelong companions, husbands and wives, will need God’s help in getting along as a result. The woman’s desire will be to lord it over her husband, but the husband will rule by divine design (Eph 5:22-25). This interpretation of the curse is based upon the identical Heb. words and grammar being used in 4:7 (see note there) to show the conflict man will have with sin as it seeks to rule him [emphasis in original].” While MacArthur concurs with the conclusions of Gill and Henry, he further demonstrates the intent of the Hebrew language which, perhaps, is lost a bit in translation. In Genesis 4:7, God is telling Cain that doing well lifts his countenance, while not doing well leads to mastery by sin. The same English words “desire is for” are used in both Genesis 3:16 and 4:7. Understanding the Hebrew helps the reader to comprehend that the desire of the wife for her husband is the same as the desire of sin for Cain: To master him. Just as the husband will yet rule over the wife in spite of her desire, so God exhorts Cain to master the sin which desires him.
Finally, in answer to the question of what the desire of woman refers, it is the want of mastery over her husband, which is yet subjected to his headship given by created order and divine decree, and exacerbated by the judgment of The Fall.
Gill, John. "Commentary on Genesis 3:16". "The New John Gill Exposition of the Entire
Henry, Matthew. "Complete Commentary on Genesis 3". "Matthew Henry Complete
Commentary on the Whole Bible".
MacArthur, John F. The MacArthur Study Bible. Thomas Nelson: La Habra, 2006.