The issue for me is that I understand children in Jewish culture take the religion of the mother, I'm considering converting for the purpose of teaching their heritage but continuing to practice as a Christian, then teach them part 2 when they are interested.
That's absolutly impossible unless you lie. You cannot become a Jew unless you are willing to give up all other religion. Period. No exceptions. Even if you did lie the Rabbis will often figure it out and refuse to work with you. In addition to lying to the Rabbi you would be asked if you are ready to give up Christianity and your faith in Jesus. You would have to say "yes" which is denying your savior. I don't think you want to do that, right?
To be completely clear, her parents don't practice either and have no illusions about needing a Jewish boy to marry their daughter, this is merely something I want to do.
It's not uncommon for people to suddenly "get religious" after they have children. Do not assume her current apathy for Judaism will always be how she feels. It's very possible after having children she'll want to raise them Jewish. How would you feel about it? If you were under the impression that maybe one day she'll be ready to convert to Christianity, give that up too. Maybe she will...maybe she won't. Just don't bet on it.
It pains me to say this but I tend to agree with Stripe on this issue. However you are already engaged so it's my guess you aren't going to call it off now.
You two may have a difficult road ahead of you. There are options but all of them leave someone having to make compromises. Good luck and welcome to the forum.