"Fool me once, shame on you. Fool me twice, shame on me."
It's time to leave... He's hiding things from you; that doesn't sound like he wants to rebuild your relationship. The fact that he still insists on having any type of relationship with this co-worker shows that he values her a lot more than he values you.
Once a cheater, always a cheater. Let her have him because if he's cheated on you, he'll wind up cheating on her. Why would you expose your children to a relationship that isn't honest? Both you and your children deserve someone who is honest, loyal and respectful. If the shoe were on the other foot, I'm quite certain he wouldn't have given you a second chance, let alone the third chance that he expects.
Of course remaining with him while the situation is beneficial to him works for him. He can have his cake and eat it too. Why would he want anything to change? In your current situation, he doesn't have to pay alimony or child support which would cramp his cheating lifestyle.