OK, well I will offer the unpopular view that I do think your wife's behavior sounds somewhat controlling. And that's about all the validating sentiment ya get. Because practically everyone I have ever known, who has behaved in controlling ways, has done so because of insecurity.
I was controlling of my ex husband's sanity because I was insecure of his ability to control himself. (Keep from violence, for instance, unless on a short leash.)
I know men who are controlling to their wives and girlfriends because they are insecure about being replaced, or about her wanting things they can't provide.
People often turn to controlling actions, when their very lives, the things that form the foundations they need to live, are shaking, in their perception.
And that, man, was all you.
If your wife "left" because she could not accept your terms, may I ask you, where would you expect her to go? Is she supposed to leave the kids for you (and gf?) to raise, or is she supposed to take them with? How will she afford FOOD, let alone everything else you need, to LIVE, for herself and three other humans?
I'm serious. Can you answer this? Tell me a story, where she and your children get a happily ever after, here. And she deserves the punishment of poverty and watching her kids suffer and be without a father, because...YOU cheated. You do wrong, she gets punished.
Can you see how it looks that way?
And how even polyamory doesn't fix that?
If you even once mentioned in this thread how you feel about your children, I could not find it. But I found several descriptions of how you feel about your girlfriend. Do you even care about the kids you helped to make?
Also, in addition to giving your wife time to adjust or whatever, let me say that YOU need time before you attempt polyamory. The health of your marriage, is not her work alone. Have you yet encountered the saying, "relationship broken; add more people"? Your marriage is a MESS and you have at least equal, if not greater, responsibility to work it out to a satisfactory conclusion, BEFORE you try to get involved with anybody else.
You owe that to your wife, kids, self, and future partners.
Also, YOU the man, you're not ready to do poly and succeed at it. Sorry. The long span of not speaking your truth, you cannot heal that in a few months' time like flipping a switch. You have a ton of stuff buried in you (I promise, and speak from personal experience) that you will need to dig up and work out.
So what does resolving the marriages issues look like?
It most definitely is NOT just waiting to give the wife a breather to accept your terms before plowing forward. OK, so you cannot wait until the kids are grown to do this. Fine. That's where you are in this negotiation. She needs a kill switch that is REASONABLE. And "ok then, leave" isn't. That one makes you look like a jackass, seriously rethink the matter of "what will she do? Where will she go? How does she support herself and kids?"
You have an obligation at the LEAST to make those things concrete realities with real answers, before you proceed to skip off into the meadow with your new love interest. You are a man, not a child. You have responsibilities. You're dismissing them, near as anyone here can tell, in some really uncool ways.
Are you personally wealthy enough to support your wife and kids AND yourself if you are living separately? Leave her the house or pay enough for her to get by? Will she be forced to quickly find a new partner to provide? Is that your plan? That could be difficult with your children in tow, suppose the only man who would be with her abused your kids, how would you feel? Women who are cut adrift like this face hardships like that, and it's like you don't even care about that. All you care about is not losing your girlfriend.
That's the picture you've painted here.
Please tell me you've given thought to these other matters.
I'm willing to accept that maybe you are not as bad (or blind) as all that, but you haven't given the forum that impression.
