When your wife comments that you are clearly always wanting to spend time with her, she gives away your most glaring weakness right now.
While I don't advocate the same as rob might, I will say that reaching out to her while she is actively pursuing another person makes no sense.
Your position was supposed to be that as long as she is seeking another, the two of you are nothing but coparents.
You can be civil, even pleasant, without appearing needy. It seems from her comment that she is NOT getting that impression from you.
Here is possibly where rob's hardcore line and my seemingly softer line meld. Your wife should not get your time and attention when she is involved with another. Keep things to business and kids.
But for goodness sake, don't implement such a thing and make it seem like you are shunning her or punishing her. It should be matter of fact, and it should be clear to her that you are MORE than ok with the status of things - that is, YOU MOVING ON TO A HAPPY LIFE and her continuing to pursue her fantasy boy toy.
Sometimes you gotta fake it till you make it, you know?
I'd say, "Sweetheart, I'm not your friend, not while you're pursuing another man. We are co-parents and I'll cooperate just fine on that end. But other than that, I'm not investing myself in a relationship when you've made your choice."
Then calmly, and oh so cooly, walk away.
Blessings,
Bill
P.S. Stop fixing her problems while she's emailing her boy toy! If she needs something fixed, she should call him. And by the way, does he sound like a great catch or what?
"Don't tell me the sky is the limit when there are footprints on the moon."