I grew up in the church my entire life. My dad is a preacher. I say all of that to give you a quick background.
I have been dating a girl for about a month now and have really started to like her. The thing is, when she was 17 she got pregnant and married her little daughter's daddy. Her heart was never in the marriage but at the same time, she was determined to make it work. After several months of marriage, she found out that her husband was cheating on her. He was a soldier and faked his deployment in order to steal money from her parents, as well as his, to fund a separate life. She left the man and moved back to her parents. She was not a Christian at the time of any of this.
She started studying the Bible with her grandfather who was a southern Baptist preacher. She then found flaws with that theology and now attends a non-denominational church. We have not discussed our faith and beliefs in full yet, but it is something that we both think is important, and we both believe a couple or family should have the same faith that the Bible teaches and should worship together. She wants me to try out her church, and I told her upfront as well that I believe strongly in what the Bible teaches, and my faith makes me who I am. Saying that, I would also like her to attend church with me and she said she would but she loves the church she attends. She even started a mom's group on Wednesday nights that she leads.
We are nowhere near close to marriage or being extremely serious but at the same time dating leads to marriage and I want to marry a Christian woman. I say all this for two reasons: One, do you believe scripturally she is a candidate for marriage? I finally told my parents about her and my mom yelled at me, asked me what in the world I was thinking, said I do not need to be desperate, and I am being stupid. My dad said she is an unbeliever and referenced II Corinthians 6:14. He has said I was not being smart, and I should not let this progress. I do agree with the fact that it is important that she be a Christian woman that follows the teachings of God through the Bible. I believe it is important that I do convert her. That leads to my number two question. How do I go about that? Can you help guide me?
P.S. A dating section would be a nice addition to the website. I love all of the articles that are scripture-based. It is an amazing help to see scripture applied.
If you want to marry a Christian woman, then you need to start there as a criterion for the women you date. Don't change your standards to meet someone you already know. At the moment, she is involved with a group that is somewhat like the church but has significant differences from the church found in the Bible. It would be useful to discuss the Bible's teachings with her, perhaps she'll see that her current church isn't following the Bible accurately. However, I would not recommend doing this while dating her. The dating relationship would make a serious discussion of the Scriptures difficult at best.
As far as whether she can marry again, that is what Jesus said in Matthew 19:9. Her husband wasn't faithful to the marriage and was committing adultery. She divorced him for his fornication, among other things, so that leaves her free to remarry if she so chooses.
II Corinthians 6:14-7:1 is being misapplied. Paul was talking about unequal relationships where a non-Christian has authority over the Christian. A marriage is a covenant between equals. It is possible for a Christian to marry a non-Christian, but it isn't advisable. You noted one problem and that being able to worship together as a family. Another problem that I'm sure you are aware of is that the odds are greater that a non-Christian will lead you away from the faith than for you to lead the non-Christian to the faith.
My suggestion is that you don't consider this relationship seriously unless she decides to follow Christ wholly. You should continue to leave your options open to find a woman who meets your criteria. If something changes in the future, then you can reassess the situation. But in the meanwhile study with her about the issues without clouding things with a relationship at this time. My guess is that you are going to find that she isn't open to becoming a true Christian, but I would love to be proved wrong.
There is a section of Questions and Answers concerning Dating and I have a section for those seriously considering marriage or are newly married. If it appears that I continue to get a lot of questions from young singles, then I'll eventually start a sub-site just for those issues as I have done for teenage boys and teenage girls.