It sounds as if you have a very good marriage at stake here and if you think it is worth fighting for don't do anything vengeful. My advice would be to try and get your children out of the house this weekend, ask a relative or friend to have them. You don't need to explain why, just say a personal crisis has come up and you need some time, or that you are ill.
Get him alone and thrash it all out with him. You need all your questions answered before you can think about forgiveness. You also need for him to see how much his actions have hurt and disappointed you. Don't bottle it up, show him how serious this is. You need to feel that he 'gets it' before you can move on.
Next, I would advise that you go to relate. They can help you communicate better. With the best will in the world, we are not experts, but they are, and can guide you to identifying the problem areas and suggest ways of easing them. They are very happy to counsel couples who are not at the point of splitting, but want to mend fences in their relationship.
Your dh needs to clear up the mess he has made without complaint and with total willingness and commitment. He needs to reassure you and give you extra love to heal the wounds he has caused. If he does all this, I am sure you will be able to get over this.
I wish you luck, and hope your future is as you wish. Please remember mumsnetters are a very caring lot and are always here for you to be listened to. Lots of love.