I am so sorry that your wife has chosen this path and has hurt you and your family in the process.
Please do not blame yourself on not following your gut. You gave your wife the gift of a second chance and she chose to disregard it. That is hers to own.
Please see an attorney ASAP to know your rights especially as it pertains to your children. She is not acting in their best interest by bringing another man into your home. Unacceptable.
Please take care of yourself and know that you are not alone. We are all here for you. One day at a time.
Sending hugs and prayers.