I'm in a relationship where I'm preparing to offer my wife a get but I expect to have an uphill battle with her accepting it. What are my options in this quite awkward situation? There won't be any custody disputes, financial support, anything, outside of pettiness, to prevent her from accepting, and as the relationship I hope to be in is outside the faith, it will not be a deterrent to me one way or the other. I truly wish to do what is best by her and the children - but will not let a document that effects her deter me.
Your approach is an honorable one, especially taking into consideration expected difficulties from your partner. You are correct in your assumption that if you do not provide "finality" to your divorce process via the issuance of a "get", it can leave its mark both on your present wife and the children.
The best thing you can do is to go to the Orthodox Beth Din (Rabbinical Court) of your choice. You can call the Beth Din of America and ask them for the one closest to you. The Beth Din will advise you of how you can arrange the get in as amicable a manner as possible. One of the possibilities, for example, is that you can leave a get for your wife at the Beth Din for her to accept it when she is comfortable in doing so. You can feel comfortable consulting with them for the rabbis there have vast experience.