People would tell you to leave him, but how easy would it be for you when you have loved and trusted this man for 10 years? How easy would it be for you to be a single mom to a toddler and soon, a newborn. Talk is cheap, people can easily tell you they will not forgive and move on. But have they been through this? They have not experienced the pain that you did and thus, it is easy for them to say with a logical mind to leave him cos he cheated. The strength it takes to leave the person you love so much, is even greater than the strength it takes to hold onto the marriage.
There are only 2 options, clearly:
1) Leave him and try to pick up your life yourself, hopefully with the support of your family and friends. Try not to think of him and the past. It will be easier to move on if your love to him turns into hatred for what he had done. However, life will be tough. You have relied on him for 10 years, and it will just be on you alone, supporting your kids. You are the one whose going to feel guilty for your kids not having a complete family, even though he should be the one feeling guilty, he won’t. You loved him for 10 years, it may take another 10 years to stop loving and thinking of him. You will never be able to cut off complete ties with him, cos you have 2 kids. And you will still see him, do you think you can stop loving him cos you still will be seeing him due to the children?
2) Forgive him. Try not to think of the past, but I know you will never trust him like you did. It was 10 years of trust, how long would it take to be built up again? Even if you forgive, you will never forget. You will always live in fear and suspicion. Things will never be the same again. Even if on the surface, you both are closer now, the wound will always hurt for you. You will always be hurting randomly. No matter how happy you get, there will always be a scar. How long does it take for a scar to heal? Does he really care if you are hurt? Cos if he did, why would he even try to hurt you in the first place?
Sometimes I don't understand how can men swear that they love their wives so much and yet still cheat. Cos they think if it's not exposed, it's not wrong since it's not gonna hurt? Where is the morals and integrity and that so-called deep love?
I can't advise which option is better for you. Both would hurt, cos what he did already caused the consequences. Truth hurts.