Hugs. I also divorced an Italian - we have 3 kids together. I avoided the three year thing (4 years really) - because we divorced abroad. (We had just moved to the Caribbean and I filed here).
I'm American, he's Italian and we divorced on a little Caribbean island. The divorce agreement is in a language that neither of us even speak. )
My xh had a girlfriend while we were still married (our housekeeper!) and then another one (his intern!)... and so the hurt was probably a good deal worse. The intern was back in Italy so he just packed up and left us all in the Caribbean to be with her. He is still with her and I DEFINITELY have the thoughts you describe. Although I do not dwell on them or even give either of them much thought. I just kind of live with the knoweldge that he hasn't changed, he hasn't gotten help, he grew up in a world where men treat women like dirt and that is what he believes women should be treated like, his dad regularly verbally abuses his mom. His dad is an ANGRY man - so is my xh - so his new gf/affair partner - well she doesn't have it good. She, meanwhile chose a gem of a guy who moves 3000 miles away from his kids to have an affair... and,l well, she was having an affair too. They can so totally have eachother. It warms my heart actually... but I digress.
What I would do in your situation: gather information. Stay sober, clear-headed and sane and USE this to your advantage. I really mean this very very very seriously. Get the agreement you want and get it signed now before they break up and while he is still in the throes of the new romance! He is not paying any attention to you - he wants the agreement signed - so don't sit around wishing bad things on him. Use this to your advantage. Add things in that you don't want and let him negotiate them out. Work with the fact that he wants it done and just focus, stay clearheaded and get it done. Do not act like you want it done, do not act in a hurry but give him deadlines, give him motivation to sign. If he is asking to get it done, though, take full advantage of this moment. And make sure you and your kids are fully taken care of. Figure out what you want and how you will get it. No drama just think of it as business and forget he is your stbxh. Treat him like you'd treat a business transaction - (no crying, no emotion just yes, no, maybe... ok sign). If you can write the agreement in English instead of Italian that would be to your advantage. I am totally fluent in Italian but xh is only so so in English. Agreement in English means he has to be even more awake - and xh (Italian men?) is lazy (expects his mother will do it for him?). It's way too much to read 4 pages of english (and Italian mom won't go there nor will she be able to read the english). Also harder for him to negotiate in english. I now send all e-mails to him in English. I still speak to him in Italian but communicate in writing only in English. He responds in both. I am sure it gives me an advantage.
Your marriage is over - it's been over and the Italian law is what's getting in the way of giving you closure. But I'd go about pretending I was already divorced. When xh left (end of 2008) - I was under the impression I'd have to wait 4 years - 1 yr of separation and 3 yrs of divorce. It seemed an eternity and the only way I'd be able to handle it would be to go about life as a divorced person. I later found out I could file here. I had advice from many people - one was picking up and moving with the kids back home, getting residence there for 6 months and filing from there. It probably is a long shot but you can speak with a lawyer from home about it. Especially if he is refusing to legally separate. Because of that you can also get help from the American (or Canadian?) consulate. That would be human rights issues. A friend who is a retired judge told me in my case doing what I just suggested "Any judge would see right through that" but in YOUR case if he is refusing to legally separate it is different. you move home, you file from home. And no 3 yr wait. I don't know if that is something you'd consider - or if you want to continue living there. I cannot imagine small village Italian life as a divorcee.
I have a LOT to say on Italian men married to American women. but that is for another thread...