The two of you need to make a concerted effort to move the arguments behind the scenes. Your children need to feel as if they have a stable home life, even when their parents are disagreeing with each other. Designate a space where the two of you can have the privacy to work things out, and then when you start to argue, take a deep breath, excuse yourselves, and resume the conversation in your bedroom or study. Consider speaking with a counselor about calmer and more productive ways to discuss your differences.
You need to tell your partner you've been unfaithful.
First examine why you strayed. Were you just craving a crush? Were you bored or drunk? Or were you trying to get out of your relationship? If you know you've made a mistake and want to stay with your man, then you're going to have to earn his trust back. It's best to tell him as honestly and simply as possible that you cheated on him and prepare for some tough times ahead.
If he's cheated on you, you need to decide whether or not it's a personal deal-breaker. If there's cheating early on in the relationship, it can be hard to know if the guy is just getting something out of his system or if he's a jerk. That's the thing about dating: At the end of the day, you're having intimate experiences with someone you don't know very well. You don't know his personal code of honor; you don't have his dating rap sheet. You have to go by instinct, how much you care about him, and what he has to say for himself about it.
Don't date any man who doesn't know why he does things. Talk things through and let him know that it'll be a slow road back to regaining your trust. And, whatever his excuse, don't ever let any man blame you for his infidelity. No matter what your relationship problems are, it's unacceptable that he should step out on you instead of confronting the issues.
You're done. It's over. You want out of the marriage.
If you've done the hard stuff -- the long discussions and the marriage counseling -- and just can't make it work, then it might be time to talk divorce. Both you and your spouse will have to get lawyers, but you might also consider hiring a neutral mediator to help you divide assets and debt in a calm and civil way. Be prepared to sacrifice some material things for your freedom -- no toaster oven is worth a bitter argument. And don't forget that a marriage is bigger than the two of you -- even if you don't have children, you have friends and family who have had a long relationship with your husband. A breakup can be like an earthquake, with ongoing aftershocks. Be prepared for him to find a girlfriend. It will happen sooner or later. Be prepared to be talked about. That will also happen. This is going to be a long haul.
If you have children, you must be as unselfish as possible. This divorce needs to be at least as much about their needs as it is about your own. While I'm no expert, I strongly suggest you seek out a child psychologist well before you make the decision to physically separate. While divorce is difficult on children, there are ways to make it easier, starting with reassuring them that your feelings about them haven't changed and that you'll do your best to spare them as much misery as possible.