How long have you been together?
Does he say he no longer wants to be a couple?
Who owns the home or is it a rental?
Do you want to leave or try and work it out?
If you do wish to work it out do you think he is willing to try?
Where is he when he is not at home? (The places he goes when your arguing about him not being at home)
Sounds like things are looking pretty bleak around the house right now. I wish I had some magical advice that would make him rethink his choices but the reality is he is going to do what he wants to do regardless of what you want.
Since you do have children together the situation as it stands right now is not going to hold for very long. A decision must be made before you both come to hate each other. I understand you want to make this work but right now with the way he is acting pushing isn't going to work. It sounds like you both need to sit down and have a heart to heart talk about where to go from here.
Let him know how you feel but that things the way they are can not continue. Either one of you needs to move on or both of you need to work this out. Since you have children this is something that needs to be taken seriously. You need to ask your self some serious questions as well. Are you planning on being the custodial parent if this does not work out? Will he be paying child support to help and if so you will need to file for this as well as a legal separation if you plan on leaving. These are all very serious matters that must be dealt with before you both are at each others throats.
I suggest a sit down meeting because at this point actions are not going to change his mind. If he is serious about not wanting to be in a relationship then it is time some decisions are made so you and the children are not sitting at home waiting on him to decide when he wants to leave. Which could happen at any time and leave you in a very bad position. By sitting down and coming up with a decision you have some control over how this happens.
If he is willing to work on the relationship then something needs to happen now....not waiting until he decides. You have 2 young children and it is not fair to them to be stuck in neutral not knowing where everything will end up. It sounds like your husband needs to grow up some and make the decisions that need to be made. While your relationship may pieces itself back together sitting around and waiting is not going to help that happen.
I can understand how that would put a damper on working on this..........though the key is to let him know that you are not just wanting to talk about working it out but talk about where you should go from here.
Let him know that while you can understand he is upset that it is time to put aside the anger and work up a plan on where you both go from here. Wither that is splitting up or working it out. You can explain to him the alternative is you leave and begin the proceedings for divorce and support. In the end it is better to just sit down and decide what you both want and where to take this.
If he refuses to talk then you may have to simply take matters into your own hands at this point. While you can stay and wait and see what happens the reality eventually he is either going to just up and leave or you will. Better to be prepared now then wait and see.
I can not tell you what to do, or even what is best for you. But as someone who can sit back and view the situation as a uninterested party I can tell you that right now you are both at a standstill.........nothing is moving forward in the relationship and nothing is getting better. In the end you have to decide what is best for you and your situation then make the choices to make the changes.