You already know the answer to your question........he has proven time and time again that he can not be trusted and that he is going to eventually hurt you again. While it would be great to say maybe this will be the last time the reality is as long as your continue to let him come back this will never be the last time.
I can not tell you wither you should allow him another chance or not. In the end it is a choice only you can make. You have to look at this for what it is, are you willing to take a chance again? Do you think he will change? Do you want to go though this pain again?
The fact is what you are feeling now is going to happen again and again and again until he eventually moves on or you finally decide he isn't worth the time of day. The hurt isn't going to stop if he does it again. But if you truly make this the last time and do not allow him to come back you at least have the knowledge you can start to move on.
As I said above I can not tell you what you should do, but I can tell you this. Until you sit him down and let him know this is not acceptable and you will not go though it again he simply is not going to get the point. Leaving you and the kids over and over in a bad situation is not only cruel but it shows he has no real love for you or the children. While he may think he loves you the reality is that kind of behavior is not love.
What I would suggest is that you sit down and give some real thought to what you want and need in a partner, then decide if he is what you want and need. If you want to give him another chance then I would suggest you start it on a trial basis. Sit him down and let him know what you expect out of him. Let him know this is the last time......be firm. Explain to him that you have to think about what your children need as well as what you need.
The reality is by continuing this vicious cycle you are never going to be able to make a good life for you and the kids. Yes life will be hard if you refuse to allow him to come back, but in the end if that is what is best for you and the kids then you need to make the right choice. Your kids must always come first.......he has hurt them and while of course it would be easier if he was there allowing him to continue to hurt them isn't doing what is in their best interest.
You have to decide what is best for your family.........no one including me can tell you what is best. You have to sit down and decide.