Most couples split for silly reasons. With some good communication they could overcome their problems and be happy.
You need to decide if you really want to get back with this person. Forget about what you want for a moment and concentrate on what you would like to do with your relationship. Once you are certain, you will be much more comfortable to talk about asking your partner to give you another chance.
If you decide that you do not want to get back with your ex partner you should have no problem getting over the break up. But I do not think you are willing to let that relationship go, do you?
You need to set up a meeting with your ex to discuss your future. Apologize for anything that went wrong, whether it was your fault or not; and agree to put the past aside. Yes you need to resolve your issues but you do not need to dwell on them.
Focus on the positives. Why should the two of you be together? Talk about the great times you have had, the history you share, the sexual attraction that burns between you and hopefully you will be celebrating getting back together very soon.
It may take a couple of meetings but it will be worth it. If you had a great relationship it is worth fighting for. Finding someone special to love who loves you in return is not easy and should not be given up lightly. Add to that a shared history, family and children and you will soon realize, that you belong together.
If there was a reason for your breakup, perhaps one of you had an affair; it does not need to spell the end. Affairs always happen for a reason. Perhaps you were not paying your partner any or enough attention. Perhaps they felt taken for granted. Or it could be something as simple as too many drinks at the Christmas/office party that end up with a flick with one of your co-employee.
I know that it is not easy to accept your partner sleeping with someone else; but you can get over it. If you still love this person and want him in your life, go to several counseling and seek help to work through your feelings. You may find that you cannot live with the deceit and betrayal and decide to split up after all. But you could also decide that by bringing all the problems into the open, you can resolve them and go forward with a much stronger relationship. You just need to approach the situation with an open mind.
Having someone you love in your life is far too important to let it go over something trivial or in some cases something very hurtful. So forget about trying to improve the "breakup recovery" and concentrate on getting your partnership back on track.