Welcome to MB. I'm sorry to hear of the breakdown of your marriage.
Mediation is our preference as we feel a judge wouldn't fully understand our situation, but I feel that if I don't let go of some of this anger, we won't be able to achieve what's best for our girls. How do you begin to cope? How do you begin to move on?
You should be wary of mediation. We often advise people here to stay well away from it. What's best for your girls, if their father is determined to leave you, is that they get adequate financial provision for their future. They need a home to live in and money for all their essentials.
The problem with mediation is that it tries to find solutions that are fair to both spouses - but what your husband considers fair to him could well be the polar opposite of what 's fair for you and the children. If you go to mediation, you are in danger of being guilt tripped into accepting arrangements that take your children away from you for half the time to live with the other woman, and that leave you broke.
There is no easy answer to how to move on. Just ensure that "moving on" does not mean that (again) you are guilt tripped into a friendly divorce, where you show your children that you are friends with the woman (and father) that wrecked their lives. You will just be more miserable having to watch their love affair play out under your nose, and having to pretend to be happy, and feeling that you are a bad person if you are not happy.
You need a lawyer to stand in your corner and fight for your rights, not a mediator.
You also need to expose the affair and make sure that your family and friends know what your worthless piece of stuff husband did to you and the kids.