I do not know the country you are living in. It is better to give her a divorce and bring a new lady in her place so that she feels the pinch of it having a boyfriend and to continue the affair even after a marriage.
In India, it is not accepted at all. People and the relatives interfere in such cases and try to compromise them on such petty issues.
It is always better to talk to her elders if they are not from any other country than India.

I am so sorry to know about your sad story of your marriage. Why has your wife find another when you already have two children? She should have helped you to make your marriage stronger. That is how during the few years in marriage somewhat shaky for you are not yet stable in your income, plus emotionally you are still adjusting life as married.Stay strong and hopeful.What you have this time is hard to define and deal having the kids far from you and you far from them. The kids need your hug and kisses and the nice words that will always linger on their minds.
If your marriage could have the chance to be repaired, do it and if not file a divorce paper so she cannot anymore interfere your own affairs. This time stay alone and single for I am so sure if there is another lady in your life, she will have a baby with you and you will have additional burden hehehe, just saying. Be hopeful and be strong not all the time skies darker most of the time clear.