Surprisingly, the commentaries I checked don't think 1 Cor 14:33 cites Gen 3:16.
One quotes FF Bruce: “This is unlikely, since in MT and LXX Gen 3:16 speaks of a woman’s instinctive inclination … (Heb. תשׁוקה [teshuqah]; Gk [LXX] ἀποστροφή) towards her husband, of which he takes advantage so as to dominate her. The reference is more probably to the creation narratives.…” Even that seems pretty weak. Another possibility is traditional Jewish interpretation of the Law. This makes more sense if 33b-35 are an interpolation, since Paul wouldn't be likely to quote this kind of interpretation as Law.
There's a lot of discussion today about 1 Cor 14:34-35, for obvious reasons. A number of recent writers think it's an interpolation. Here are the arguments (from Senft and Schrage, summarized by from Thiselton's commentary on 1 Cor. Thiselton obviously doesn't think much of them):
(1) The verses allegedly differ from the main theme or themes of 12:1–14:40; (2) they supposedly interrupt the flow of instructions about the prophets, as the Western copyists perceive (and a few MSS place them after 14:40, e.g., D, F, G); (3) the verses contradict 11:5; (4) to appeal to “the law” to endorse or to validate church discipline is “non-Pauline”; (5) “the expression ‘the church of the saints’ [ταῖς ἐκκλησίαις τῶν ἁγίων, translated above as the churches of God’s holy people] is foreign to Paul.”
I don't think this is a majority view, though it has a number of distinguished defenders, e.g. Gordon Fee. Fee is a textual expert, and most other commentators aren't, so one might want to weigh his expertise heavily.
Another view, which is pretty common, is that the objection is to women talking in church, i.e. interrupting the service. There's an implication that they are talking to their husbands, who might (in accordance with Jewish custom) be sitting in a separate section of the meeting. (I note, however, that we don't actually know what form these house churches took. It's not at all clear that they actually were like a Jewish synagogue.) That's the position I think is most likely. I don't believe Paul is opposed to women talking in an authorized fashion, or 1 Cor 11:5 would make no sense.