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Tantumergo already replied with some very useful observations. Let me just also point out that your situation is difficult because you are taking 2 different issues which are both inherently complicated, and combining them together, multiplying the complications.

On its own, the annulment issue is already the issue that occupies the vast majority of church canon law time. These can be very complicated procedures, even for people born Catholic. You may have heard of the book written by the former wife of one of the Kennedy's, Sheila Rauch Kennedy was her name I believe, and another book called "The Annulment Crisis." The pope has recently spoken out strongly to the Roman Curia, the "court of appeal" you might say, about the need for them to tighten their criteria for granting annulments. So this is a huge issue throughout the Church, on the invidual level for those seeking annulments, and on the national level because of the geometric expansion in the number of annulments granted.

Then you have the conversion process, which is normally a major issue all by itself, even when you are not seeking two annulments. There is the question of the RCIA process which is extremely controversial due to the fact that most RCIA programs are little more than mis-education in heresy. And there is the broader issue of one's conversion and one's religious experience that has led you to this point.

So taking all the complications from both of these issues and multiplying them together is going to create a situation that cannot be resolved overnight. Ultimately, however, it boils down to the question, "Are you living in sin?" Both you and your wife have former marriages and living former marriage partners. Jesus says very strongly and clearly that "A man who divorces his wife and marries another commits adultery, and the same for a woman." The issue that must be resolved is, "What does it mean to become a Catholic if you are living in adultery and intend to continue living in adultery?"

It's not impossible that this could be resolved, but it's apparent why it must be treated as an extremely serious situation, and why it cannot be dismissed lightly, and why these issues are going to strike to the heart of your conversion experience, one way or another.