Hi, I'd like to help you with your problem.
I am so sorry you are going through this. From what you wrote, it sounds like your husband is having issues with your marriage and has cheated on you with your best friend and a supervisor. You say that given that you still would like to continue in the marriage.
When affairs occur in a marriage, it is a difficult time. The partners, especially the one being cheated on, need to decide if the marriage can be saved. If both partners agree to try, the one cheating needs to stop the behavior. Trust needs to be rebuilt. To build trust, the couple must work closely together to establish rules that are fair but also give the non cheating partner reassurances that the cheating partner is not continuing with the behavior.
Although you can accomplish this together, I highly recommend that you both seek marital counseling to find the reasons this is occurring in your marriage. Working with a counselor will help keep things fair and the issues can be discussed easier without possible additional issues coming up.
If your husband will not go to therapy with you, go without him. You can only benefit from the extra support and help with working out your feelings about the situation. Also consider including your children who may have strong feelings about what is occurring between you and your husband.
I am concerned that you feel this affair is your fault or even the fault of your children. Whenever there are issues in a marriage, there are many ways of working them out without involving an affair. An affair shows disrespect to your partner and breaks the trust and vows of the marriage. Often, it ends the marriage. The damage to the non cheating partner and the children in the marriage can be great. And your acceptance of the blame may be seen as permission for your husband to continue the behavior. Please consider working with a counselor on this issue.
Here are some good books to help get you started with healing. The first one is Getting Past the Affair: A Program to Help You Cope, Heal, and Move On -- Together or Apart by Douglas K. Snyder PhD, Donald H. Baucom PhD, and Kristina Coop Gordon PhD. The second one is Not "Just Friends": Rebuilding Trust and Recovering Your Sanity After Infidelity by Shirley P. Glass and Jean Coppock Staeheli. There are many more resources available to help you get started on the road to recovery from this trauma.
I hope this has helped you,