It seems like you know what the Bible says, but you don't know what it means. So let me break it down for you. Hermeneutics goes a long way, understanding what verses were written for, and who they were written for, during the time and culture.
The whole of 1 Timothy 2:11–14, quoted only partially above, is this: “A woman a should learn in quietness and full submission. I do not permit a woman to teach or to assume authority over a man; she must be quiet. For Adam was formed first, then Eve. And Adam was not the one deceived; it was the woman who was deceived and became a sinner.” Note that Paul specifies the subjects of teaching and assuming authority. A woman is to “be quiet” in that she does not teach men in the church, and she shows her submission to authority by learning. In other words, this is not an absolute command for women to remain silent at all times in all services.
Taking a closer look at 1 Corinthians 14, we see the overall concern is orderly assemblies. The church of Corinth was noted for the disorder rampant in that assembly (verse 33). It seems that everyone in the church service was participating whenever and however they desired. Those with the gift of tongues were speaking simultaneously, and no one was concerned with interpreting what was being said. Those with a supposed revelation from God were shouting out randomly, even if what was said could not be heard above the din, and apparently no one was evaluating what was being offered as prophecy. The meetings in Corinth were characterized by chaos, and no one was being edified or instructed (see verses 5, 12, and 19). To remedy this, Paul instructs a number of groups to “be quiet” at certain times and under certain conditions:
• Verses 27–28a, Those who would speak in a tongue must “keep silent” if someone else is speaking or if there is no one to interpret what is said.
• Verses 29–31a, A prophet must “be silent” if someone else has the floor.
• Verses 34–35, Women should “keep silent” to show proper submission.
1 Corinthians 14:33-35 appears in a very specific context. Most of 1 Corinthians chapter 14 is a discussion of tongues and prophesy. The immediate context of verses 33-35 is the evaluation of tongues and prophesy. Women are to be silent in that context.
In 1 Timothy 2:11-12, women are prohibited from teaching and exercising authority over men. In 1 Corinthians 14:33-35, women are prohibited from participating in the authoritative evaluation of any revelation given in tongues or prophecy. Doing so would involve exercising authority over men.
There are many roles women can fill in the church. The only roles women cannot fill in the church are ones that involve teaching or exercising authority over men. The evaluation of new revelation given through the spiritual gifts of tongues and prophecy would involve exercising authority over men. Therefore, when tongues and prophecy are being evaluated, women are to remain silent. Interpreted in its context, 1 Corinthians 14:33-35 is not a command for women to be silent at all times in the church. Rather, it is a command, in agreement with 1 Timothy 2:11-12, that women are not to exercise authority over men in the church.