Sorry you are here under these circumstances. You have to be calm and clinical. Do not threaten or cajole her.
For her to demonstrate how serious she is, she hand writes a no contact letter to the OM ( other man) sample below. Sample No Contact Letters
You then send it certified post to him and a copy via text message.
She may say no, ensure she understands that this is for you to help recover from her deceit. She may decline do not force her she should do this willingly.
Do not believe she called his real number it may be a preplanned number with his voice mail at the end. Check the details against the bill.
Book an doctors appointment for her to have an STD check , use her normal doctor, then you confirm the appointment with her.
You find the details of the OM, is he married, has children etc..
You let his wife and children know he is having an affair with your wife. Do not mince the words if you need some words post and they will be provided. This is not revenge this is the recommended process by Harley from marriagebuilders.com
Do not believe a word your wife says,about it being over, she will lie. Your wife seems rather secure to be sitting laughing at the TV after committing adultery. You have to be absolutely certain this is over before you start trying to recover the marriage.
One of the recommended steps is to tell your children of the affair. There are other steps to follow I suggest you read the articles under the MB site. Articles
and affaircare site Articles
Many will tell you not to tell your children and leave things as they are.. I am advocating a processes set out by Harley to ensure the affair is over and the marriage can recover that include you being able to recover.
Buy the following book:
Surviving an Affair by Harley... both of you must read this..
If she had sex in your marital bed,or guest bed etc.it is a trigger for you, dump it and all the bedding and she can help get rid of it. You must not have the triggers in your house.
Check your accounts are secure and no moneys have been moved out.
What I can't get from your post , did she show remorse, cry etc..
For now be very strong for yourself. Post regularly and ask any questions.