@Jeannnnie,
1. Why would you want to stay with someone who obviously has commitment issues? He has been disrespecting you for years and would likely do this to any woman he is with. He is not for you. Get out and on your own. Even if you have to go on welfare, it's going to be better, mentally and emotionally, than living with such disregard and disrespect.
2. Leaving will be the best thing for your children. Their dad may or may not be in their lives, but they won't be learning disrespectful behaviour.
3. Don't even think about finding another man. One - most won't want to take on 3 kids, Two - you need some time to readjust your opinion of yourself, and Three - you need to figure out what you're going to do with your life. Spend time with loved ones, read some books, play with your kids, cook interesting food, make your life about you, your kiddies and your friends and family. It can be extremely rewarding.
You married a bum. Realize it and get over it. We all make mistakes - don't beat yourself up about it. Just Move On.