BOTH NON-CATHOLIC

I was writing in hopes that you might be able to
answer a question I have regarding annulments in the
Catholic Church. Let me give you a brief summary of
what happened and then I'll end with my question to
you.

I was married for the first time back in November
1999, in a Protestant church, both of us non-Catholic.
Yet at the time I can honestly say that I was not in
love, but rather felt it was what I was supposed to do
having dated the girl for nearly two years (I was 24
years old at the time.) After 1 1/2 years of marriage,
she finally admitted to me that she was having an
affair with someone that she worked with and did not
want to be married to me anymore. At this point she
stated that she wanted a divorce from me. I had
attempted to work out the marriage as I felt this is
what God would want, but nonetheless she wanted me to
file for divorce (why she didn't file I still do not
understand.) Now I received my civil divorce in August
of 2002 (we were separated since summer of 2001.) I
had been dating a woman while the divorce process was
going on (which now I think perhaps I should have
waited until the first marriage was dissolved.)
Anyways, after the divorce was granted, I knew that
this woman I was truly in love with and we got married
in a non-denominational chapel in September of 2002.
Neither of us were Catholic at the time either.

Now it is three years later and my second wife and I
are wanting to join the Catholic church and I am of
the understanding that I need to file for annulment
before the Church will recognize my current marriage.
Also, I have had my first child from my current
marriage, so I know that this marriage is one that
both my wife and I want to build upon God and the
Church.

My question is: Does my situation with my first
marriage sound like I could file for an annulment due
to adultery committed by the first wife and the fact
that she wanted to leave when I was attempting to work
this thing out if possible? Any insight to this
question would be greatly appreciated.