@Eddieharvey,
So what you're saying is that you don't want him to be telling the truth because then you would have to stop punishing him.
Is that what you mean? Because I'm pretty confused now.
Can I ask how old you are?
You do realise that it is fairly normal for people who have children together to maintain some degree of contact, don't you? Whether you like it or not she will always be the mother of his children, so if you can't accept this and trust him then there is not much hope for your relationship. I get that he lied at first, but it seems that you actually want him to still be lying.