10 years with lover/2 kids back to wife

I've watched a TV show yesterday that I can't forget yet.

Family with 25 y/old son, famous, same financial status.
Happy, however friends noticing when they are traveling sometimes they are staying in different rooms or even hotels.

One day TV show comes where lover woman tells it all that he has an affair with her for 10 years out of which they have 2 sons 9 and 3 y/old.

He was seducing her for months sending her flowers to her office and she was denying him until she fell for him.

He is great father (people are saying). We see how he is cuddling with kids, reading bed stories and seems pretty happy.
They had traveled all Europe together.
(His lover is also having demanding well paying job).

So after she told it all on TV man returned to his wife who made him refused his children.
He is telling from the TV screen about refusing to be a father to these 2 boys.

Family goes on living.

Lover woman never filed for alimony nor she asked for inheritance (man died). So wasn't in it for money.

My question is about wife.
1. Who needs a man like that back?
2. How can any woman make her husband abandon his children.

About husband.
Why to have 2 kids with lover if you are loving your wife?