Dude, when I first read in the OP "She is fairly cold to me" I thought to myself "she doesn't love him anymore but loves the other guy". Then reading though most of what happened after, its clear that it was over for her long ago.
I mean even things here like: "She says she needs time to think things through" yeah, want to split up, wants you out but can't say it directly due to cowardness. do you think she would want that if she loved you?
"She says she wants us to be an Eternal Family, but that I am not respecting her by leaving her for a month or more" ....she's lying! She wants to be an eternal family with someone else! Then in saying that you don't respect her by leaving is just a way to blame the victim and/or get you out of the house so she can see the other guy whenever she want to. Remember that adultery and lies go hand in hand, you can't have one without the other.
"She shows no affection and snubs any I try to give her" ...yeah, because she doens't love you and probably is madely in love with the other guy so she never will want to be touched by you.
Look, I've been in your situation. It took me more than 2 years to come to terms with it. But once it's over like this and she no longer loves you, just forget it. The best you can do is divorce her as quickly as possible, pay what the law requires and start looking for someone who will love and respect you and wants to be around you. Don't make the mistake I did in loosing 2 years crying over someone who doesn't love you. It isn't worth it.
Your relationship had become toxic long ago and now, dear brother, the best that can happen for you is that you start seeing someone new and start from scratch. Like I said, don't make the mistake I made and loose 2 years or more hoping to fix things up...they wont. the pain takes a while to go away but it does eventually. And the sooner you are going out to SA activities and meeting new people the sooner the pain will go away too.
Best wishes...
John.