I dont know if that was "dumping her" as much as it was instigating anger in her. Everytime I have ever been dumped it was pretty much like pulling teeth just to get a response as to why 'she' was not talking to me any longer and then the response I remember was always 'oh, I gotta run, talk to you later," and that never happened.

So, yes, you are mad, maybe want to get even, sick of limbo and want to get your marriage reconcilled or maybe move on without her. I still dont see it as being that great of a move to brag or lash out that you went on a date. It appears as just that, bragging, lashing out, revenge. A hurtful attempt that can be brushed off as petty. The greater sense of loss and jealousy comes when you walk-away without a sound. When they harbor the questions in their head, why dont they talk to me? Is he/she seeing someone else? I think the are. Are they having sex? They must be. It eats away at a person. It is all they begin think about and want. It ate away at you. Why? Because you are human.

It is also then that you will experience the greatest level of freedom and detachment. You no longer have the consideration, this may work as Gucci says to save my marriage. It becomes all about you. When you no longer care to do what works you have nothing to left to say. "When the well runs dry there is nothing left to say." Enjoy interacting for you. So what if you are sneaking and hiding something from your spouse. Once you start paying lawyers to divy up stupid toys, 100 dollar beds, linens, towel sets and pots and pans, playing nice in the sand box just isnt happening any more.

Not so much as advice then what I have realized through personal experience is now that the cat is out of the bag, so to say, is to continue 'interacting' for you. Do not to flaunt it; dont talk about it. If it comes up always admit to one level less than what is actually happening. "We are just friends." I love that saying almost as much as "You are right, this isnt working."
In fact why talk about anything anymore. Be mysterious and your own man. I dont know if you are truely using this as a LRT to get your wife to reconcile or if you are looking to find yourself a girlfriend. But have you ever noticed that the guy with all the girls is the one who can still attract more girls.
Time to be a stud.

Oh, and I would think that if your wife lashes out in anger and uses the children as pawns, she has issues, I would immediately bag on the Mediation and hire an attorney of my own, one that has a high success rate in acquiring equal custody for men and pursue a custody agreement immediately.