I was born into a Catholic family, baptized, received Communion, and confirmed in the Catholic Church. I was married to a Protestant in a Protestant church with a priest present to bless the marriage, left the Church, regrettably, was divorced and remarried, and now, because of objections from my Protestant wife (more out of fear and confusion than from hatred), I cannot receive an annulment (we actually have a very good marriage). I am forty, and as far as I know in good health, but If I were to die, could I have a Catholic funeral?
To answer the immediate question: Yes, of course you can have a Catholic funeral. All you need do is put such a request in writing and attach it to the documents you have prepared in the event of your death. For that matter, should the need arise, you could even be reconciled to the Church on your deathbed by promising to live as brother-and-sister with your wife. However, that is not the question that should be under consideration right now.
The question that you should be asking is what you can do to regularize your marital situation in the Church. If you feel that your wife is confused and fearful of what the annulment process might mean, then the two of you should do some research on the subject. A very helpful book is canon lawyer Edward Peters’ Annulments and the Catholic Church. An appointment with your local pastor to discuss the process and answer questions would also be in order. You can also call Catholic Answers directly at 619-387-7200 for more personalized assistance.
Fear is a debilitating thing that prevents us from finding solutions. Just as fear of doctors can lead a patient to avoid treatment that might save his life if given in time, so fear of religious leaders can lead a soul to avoid treatment that might save his spiritual life. Of the two, the second situation is far more serious because it can lead to eternal death rather than bodily death. That is why one of the themes of John Paul II’s papacy was Christ’s admonition to “Be not afraid!”