Welcome to our forum.
"I will either have to find a way to come to terms with the fact that he has somebody else, or I will have to leave him."
There is also the option/possibility of talking him out of seeing this other woman. But that involves something he controls: his actions. You can ask him to change his actions, but only he can decide whether he'll actually do that.
I gathered from your first post that he originally promised he'd break up with this other woman if you asked him to. A few months later, you did ask him to, but he did not comply -- either because he couldn't, or because he didn't want to. Either way, he failed to keep his promise.
So I guess I am skeptical about whether it would be possible to convince him to leave this other woman. His track record indicates that that just isn't gonna happen. Whether that means the other woman is more important to you is something of a riddle. It could mean that both women are equally important, he is tore up about it and can't bring himself to leave either woman. Or it could mean that he just isn't keeping his word to you.
Underlying all this, somewhere, I realize, is the idea that all people have a right to a faithfully monogamous spouse. Your husband has not been faithfully monogamous, so you have been "robbed" of that right. As this is a poly forum, we could probably end up with a long thread arguing about whether monogamy is a right. Some people think polyamory is a right. I don't think either position greatly matters here. What matters here is that you need one thing from your marriage, and it looks like your husband needs something else. The two needs are not compatible.
If you stay in this marriage, you will essentially be denying your own essential need for monogamy. You will (by staying) be condoning your husband's relationship with this other woman. I can't sugar-coat those realities because the rest of your life is at stake here. Do not stay in this marriage unless you are 100% sure you want to do so.
There's always the chance that you might get used to this other woman being in the picture, that you might eventually find yourself able to be at peace with polyamory. If so, great, and sticking with the marriage would certainly be worth it if that's the outcome. I guess the question is, how long do you think you should give this process before giving up on it? Since it might never work, you are gambling another year of your life for every year that you stay in this marriage. There are, after all, other men out there. Men who would be truly faithful to you.
But, you should probably try to decide on a reasonable time frame. What would be fair in terms of giving this poly thing a chance to work? I would roughly estimate a year, but that is a highly inadequate estimate as people are so unique and individual, and a year may be nowhere near the right amount of time for you. Ten years might be the right amount of time for you. Ten days might be the right amount of time for you. You can of course (and should) get perspective from this site on that sort of subject, but ultimately the decision has to be yours. Remember, we are now talking about your actions. That's what you can control.
I am sorry that you have invested almost 20 years of your life into something that has turned out to be a heartbreak for you. You are a good person, tried to meet your husband's needs, and didn't deserve this kind of pain. We can only try to decide what to do about it, now that it's already happened.
I might suggest you do some reading on various threads on this site, and glean some perspective in case it might help you get your bearings. The Life stories and blogs board
might be helpful, as it describes real-life poly situations in detail, how people coped with various things, and what did and didn't work.
In any case, I hope things somehow turn around for you so that you can eventually be happy.