Reading the words you write is like seeing my own thoughts put down on paper. I will try and give you the advise that on my good days i am able to put into practice.
Pack his things and ask him to take them. If he doesnt, then put them somewhere you cant see them. Any photos you have of him in frames with the kids put in the childrens room so they know that he is still a part of their lives. It hurts like hell as he has been such an absent father but he will miss them before he starts to miss you, and you will know that youve done the right thing by not playing the kids against him. He will try to put that on you too - dont give him ammunition.
Like you I dont think my H is the type of person to come back. He is proud and generally unwilling to say when he has made a mistake. Right now he is doing everything he can to prove he did not make a mistake. So, it will be hard for him to admit, when the fog lifts, that he wants to come home. I try not to think about whether that day ever happens and what I will do if it does. I try and live each day as fully as i can. I try and find beauty and pleasure in things. I try and be present. I try not to think about him. I try and not do anything i would be ashamed of or regret.
This will effect the kids. Maybe not the OW part specifically but everything. They will sense your anxiety, your fear, your anger. When it rises, leave the room. Take five minutes to breath. Get a mantra (mine are "dignity and grace" and "accept things as they are") and repeat it to yourself. I bought a crystal necklace with an unconditional love healing stone. I dont know id I put much stock in it but I touch it when the anger or the doubt rises. It is not just unconditional love for him, but also learning unconditional love for myself- be kinder to myself, accept my faults, and love myself anyway. It calms me down and reminds me that even if i lose him, I will have found me. The kids will be better for having a mother who is less anxious. you will show them that you are ok which will help them be ok.
And lastly, he will continue to jeckle and hyde on you. Be strong. Only you know how much you can take. Listen to friends but only take the advise that feels right to you. One day he may want to come back. One day you may not want him back. In either case, youre doing what you need to to heal and you can say hand on heart that you did everything to protect your children.