What should I do when my wife, a non-Catholic, says I am trying to force her to convert whenever I try and have even the most subtle discussions about faith?
Perhaps it is time to reconsider attempting any discussions about faith. From your description of the situation, it sounds as if your wife believes, rightly or wrongly, that you are trying to convert her, and she is resisting that. She probably sees these discussions, however artful your rhetoric, as pressuring her to become a Catholic.
While discussions on faith are helpful when both parties are open to such discussions, they can become a hindrance when one party believes the other is engaging in unjust proselytism. For married couples, this can be even more serious if pursuing the discussions puts a strain on the marriage. This doesn't mean that you should stop praying for your wife or stop hoping for her conversion. It means only that it might not be a good idea to discuss issues of faith with her at this time. If she becomes open to them later, then you can resume discussion.
In the meantime, I recommend reading The Children of Many Tears, a blog post I wrote on how to work for the conversion of loved ones. I also recommend The Secret Diary of Elisabeth Leseur, written by a Catholic woman who prayed for many years for the conversion of her atheist husband. Only after her death did he revert to the Catholic Faith and eventually became a Dominican priest.