I think that it is very good of you to consider the family. Although my parents have always been together and have never had any problems with affairs and so on, many of my friends have either been divorced or their parents are divorced. It is not a pleasant experience for either the child or the ex-spouse. I feel very sorry for you, and for what the children may go through in the future.
Do you go to a church? That should be the first thing to do. Any married couple that puts God first and foremost in their lives and marriage is bound to stay together with no problems like what you have been through. About one in ten of my friends outside of my church have divorced parents. There have been no divorces in my church. Think about it.
Please put yourself in your husband's and your childrens' and the other woman's shoes. Though your spouse and the woman may have done something very selfish, they have feelings as well.
Do not avoid talking about this with your husband. Perhaps when the children are away and when you two are alone, confront him in a kind but firm manner. Do not justify what he did, but do not put him down for your own satisfaction. Let everything that you say to him be for his own good and your childrens'. State that he should not see the other woman again, but do not add an "or else" to it. Also, state this:
Love is patient, love is kind. It does not envy, it does not boast, it is not proud. It is not rude, it is not self-seeking, it is not easily angered, it keeps no record of wrongs. Love does not delight in evil but rejoices with the truth. It always protects, always trusts, always hopes, always perseveres.
You should be patient with him while he repents of his sin. You both should be kind to each other despite your past. You should try not to be envious of the other woman but be compassionate. He should not boast in arguments of the times he had with the other, and you should not boast of how you deserve more than he. You should both be humble enough to change your ways, not proud. You should speak to each other with loving and not rude words and respect one another. He should not be self-seeking by being with her again and leaving you, and you should not be self-seeking by leaving him. You should not be easily angered with him for how he sins against you. Do not keep a record of his wrongs but forgive him and be compassionate. Neither should take delight in evil but instead rejoice in the truth, as in rejoice in each other's good points. You should always protect one another, (believe it or not) always trust one another, always hope for your marriage to go uphill in the future, and your love should persevere and you shouldn't leave each other.
Go by this, and you will realize that love never fails.
However, if you are not able to save your marriage, please divorce him because of his unfaithfulness, and for no other reason. Despite the doctrine of many churches, it states clearly in the Bible that divorce for any other reason is sinful, and that God hates divorce in general.
Good luck, and tell me how it goes.
