It's all well and good for me to say to you WELL LEAVE HIM, but I sense your from another country and that women from your country have been brought up with different idea;s about marriage etc, for example as the people of India and eastern countries. If is not the case and your more westernised, then you will have the same sort of beliefs, which mainly is men do not own women. Even if you are from the Western side of the world, it's not really right to tell a person what to do. There's an old fashioned saying which is '' do not judge others until you walk in their shoes'' and if you think about that you will know exactly what it means.
Yours is a very sad situation, for he has in your 23 years of married life betrayed you all through these years, and to say he stayed just because of the kids was a very cruel thing to say to you. Men can be so hurtful. Try not to be too hurt about that remark, for the truth it, he did not stay just because of the children, his fancy women were only out for fun, they would not have taken him on. For if he feels a woman is a husbands property, then so does he feel the same way about his kids. It is him that was not good enough, NOT you.
As I have already said, we should not tell you what you should do, for if we do, we are going on our own feelings. Part of me wants to say leave him, and get as much money out of him as you can so that your future life can go on in at least financial comfort, but again I am not walking in your shoes. People that have been married for a long time, feel the pain much deeper than those that have only been married a few years. It's not just the pain of the person you love leaving you, its all those years you spent with that person, its the style of living that you have to loose too, all the hopes and dreams you put into that relationship, you feel he has stolen all those years from you, and he has. You have to move, children are involved, life changing things will happen to them too, new schools, losing old friends, things that should not be happening to them. The person that cheats not only hurts his partner dreadfully he hurts others too, namely his own children.
I would suggest though that you do not rush or make him rush you into a situation, like telling you to leave the home, Go and get a solicitor or Lawyer and get good advice. You have not broken the marriage vow, so make him pay the price for doing that to you. Start going out with friends, if you have had any that is, I imagine the man pretty much governed all that you were allowed to do. But start at a college for something you would like to do, or something social like that, for then you will start to find new friends. Treat yourself to a totally new image, new hair style, change your style of clothes, all these things will build your confidence up. Don't rush into a new relationship too soon, you may feel that this will never happen because that is not what you want to do, but in time you may well want to settle down again, especially if you meet a man that shows you love and respect.
Just take your time, get good advice. You will get over this hurt, but it will take time. Remember there is always light at the end of any tunnel. I wish you well and know eventually you will fine happiness again, which does not mean to say that will be via a man. Women today enjoy their freedom, they may be career minded, and they turn their lives to that. Just be you, enjoy finding the real you. This awful period in your life will not go on for ever - but don't be second best to him, he has treated you very badly.
Good Luck !