I took the time to read through your polyamoryonline thread, and I will have admit to being a bit flummoxed.
Obviously, your wife is in a long-term relationship with another man, one with whom your wife can maintain an indefinite romantic- or fantasy-only relationship with. With him there is none of the messy day-to-day errands, house clean-up, bill-paying, kid wrangling, space-sharing interactions and compromises that go along with an actual spouse. He's the romantic get-away and the confidential friend ONLY --> a win-win for him, as there's less chance of any *negatives* being attached to him as long as he romances her and maintains the emotional connection with her.
Based upon this statement:
"I'm glad we're in a poly relationship since I can get the needs met elsewhere."
You've gone outside of the relationship with your wife as well, and can enjoy the same advantage I've mentioned above. Your wife can be your practical, kid-raising partner, while your other woman can be your romance and fantasy girl. It's all out in the open, agreed to by both you and your spouse, and you each have each other's blessings.
I'm not really surprised to see a poly relationship devolve into the above his and hers respective OW and OM. In my observation, human beings tend to be serially MONOGAMOUS, in that we tend to form one romantic attachment at a time -- and your wife has found her current romantic interest in the other man. Women, in particular, tend NOT to separate emotional closeness and intimacy with physical closeness and intimacy: the two occur as a package deal (men are a little more successful at achieving this separation, but once we fall in love, the package deal is there for us as well).
So where does that leave you? In direct romantic competition with the other man. And YOU come with a load of past baggage and practical compromises that HE doesn't have to navigate. You even have your past physical appearance to contend with in her mind (she may wonder if you'll go back to your previous unfit state at some point). You've got the odds stacked against you for winning back her attentions. I hate to say this, but you opened the 'open marriage' can of worms in the first place, and in so doing, set yourself up for this.
I honestly don't know what to advise here, because my own relationship philosophy, experience, and studying has involved only exclusively monogamous relationships (one man, one woman). You might take a read through Michele's The Sex-Starved Marrage and look over her articles and books that cover affairs and the feelings / complications that go with them. Otherwise, see what advice the poly-amorous, open marriage, or swinging discussion groups can give you --> I'm sure yours is a not uncommon situation.
Good luck,
-- B.
Me 50, W 45, M for 26 yrs S25, D23, S13, S10 20+ year SSM; recovery began Oct 2007