This post actually got me to sign up and quit lurking. Y’all are going to be sorry!
The OP has obviously been hurt. Divorce does that, and that’s why God hates divorce. Been there, done that. Tried to reconcile, the whole works. Your spouse could have “converted” but the proof is in the pudding. And that’s why the Church rules are so very important.
The Church is your mother. Listen to your mother. (I have a vested interest in this, being a mom myself.) I went through the annulment process. It was long and drawn out because an obstinant ex delayed the divorce HE sought and dragged out the civil divorce over a period of 7 years before I finally had a civil decree. Next day I was at the parish office picking up my annulment packet.
If you’ve been through an annulment, it’s not for the weak of heart. And it’s extremely helpful to healing and gaining perspective. And until you go through it, you are NOT ready for a new relationship, no matter how shiny and pretty it looks to you now. You must behave as if you are still married, whether the ex does or not. This is about YOUR relationship with God.
And if that new woman is of any lasting value, she will put your spiritual needs before companionship needs. Her behavior and patience (remember… LOVE IS PATIENT) during this time will tell you whether she is gold, or just glitters like gold. You need to SEE that she can respect and follow rules and isn’t burdened by commitments and vows and God’s law. Wasn’t your problem with the ex that she was lacking in this manner? Let Mother Church help you to test this.
As for cohabiting, just a word of advice.
If you can live together chastely for the long time it takes to go through this process, you probably don’t belong together in the first place. 
:crying: :bigyikes:

uch: And if you put yourself in the occasion of sin, you have only proven to each other that you and she lack self control. Haven’t you already suffered from this torture with your ex? That instills the kind of fundamental doubt that will come back to haunt you later.
Follow the rules. They will protect you from divorce #4.