No, I'm not here to agitate or anger you. I simply mention those points bc that might be what your wife is thinking....it will help you see another perspective.
The good advice people are giving is diverse, so you pick what works for you and your family and what doesn't. But if you don't know what to do, here's some -
Some people say avoid deep relationship talks for a while. And that might be true, but this is something that will absolutely help, even though it might not be this week, month, or even this year.
Ask your wife this:
What is the question she wants answered that she's afraid to ask you.
That is, there are some questions that you just need to know to heal - to hear it outloud - that will help bring you closer (or break you up).
It doesn't matter if it's a man or woman. I've seen lots of great guys go through emotional nightmares from their cheating wives. One question a friend needed to know was that the bikini waxes his wife started getting WEREN"T FOR HIM. That helped him emotionally even though it's a brutal truth. Another man needed to know if his cheating wife did it because he didn't make enough money. She told him that she had pawned her engagement ring almost 18 months prior and replaced the diamond with a cubic zirconium so she didn't have to feel controlled by his money. Cold.
Men and women can be equally cruel and have different needs for their recovery from infidelity. For one of these stories, they stayed together, another they didn't, but it doesn't matter which one is which. Both cheated on partners needed a specific, heartbreaking question answered.
A friend who is a woman needed NOT to know the details from her cheating husband. She didn't want any details at all.
I needed to see the emails he used to solicit sex from the OW. Looking back, one really important line he wrote became my mantra that gave me the strength to divorce him without changing my mind. He wrote to the other woman: My kids would love you.
He told me that the OW was an awful, ugly, mean woman but that's not true.
I don't have an ax to grind again men.
I have an ax to grind against liars.
So ask your wife: what part of the lie you told her does she need to know the truth about.
It might just help you to offer it instead of putting the burden on her since she's (obviously) got a whole lot of other things to consider (like if that bikini wax she's been thinking of is overdue, maybe your wife wants to have sex with other men too).