First, I am sorry for the pain that you have. We have to very clearly distinguish between your reconciling with and forgiving your husband. There are important differences. The most immediate issue is reconciliation, which is when two or more people come together again in mutual trust. The basic question is this: Can you trust your husband now and if so, what is the evidence? Trust usually is won after a series of steps to rebuild that trust.
The second issue is forgiveness. You and the children can begin today to forgive your husband/their father. When you forgive, you are working on reducing and even eliminating your resentment toward him and offering mercy, which may or may not include a welcoming back to the marriage.
We have??resources in our Store for children and early adolescents who wish to learn to forgive. My book,??The Forgiving Life, may be helpful in your forgiveness journey. I recommend that you forgive your husband for each injustice that particularly has wounded you.
Forgiveness is a journey that can take time, so please be gentle with yourself and please allow the children time to be angry and to grieve because for some time now their family has not been intact.