Treese, Let me say this...you have not failed. You fought for your marriage, but your h is a lost soul who instead of facing his demons, ran. He is the coward in all of this, he's the one that failed, not you.
As for your children, they are your most supportive cheerleaders in all of this. Yes, all of you will have days of being emotional, but you need to feel those emotions and then let them go. Each time you have a spell, once it's over and done w/it should be making you stronger, not weaker.
As you go along, you will discover that there are many things that you can do yourself and not rely on him for them. As you make progress, step back and take a look at what you have accomplished. That should give you the most wonderful feeling...you did it yourself.
Now, pull yourself together for you have a lot to to think about, write down and be ready to deal with come Tuesday. Just remember, leave your emotions at the door, for this is now a business deal that needs to be taken care. Do not allow yourself to be backed into a corner and whatever you do, do not go soft and opt to agree w/things if you know you will need a certain amount of money or things from the house. Stand firm..you are doing this for your family and for you. He gave all of that up the day he walked out the door.
You will make it, but it's going to be one day at a time for a while.