bornagainbeliever,
Blessings to you. You have my sincerest prayers in this situation.
I would like to offer something a bit different. I would like to encourage you to really pray for your husband daily, and build him up. The book, "Power of a Praying Wife" is very good to help with this. It is inexpensive, and helps you pray, when you don't know what to pray...or, when you are so distraught that you can't pray. I know it is hard to have respect for someone when their choices seem foolish...and indeed will have consequences, but you must. He is building a pile of regrets, but God can turn it into wonderful blessings.
I am afraid that making demands, setting boundaries, and possibly harping or fussing could place him a position where he does not feel like the head of your home, and is not getting respected. He does not have to obey you. He deserves honor and respect because of his position, not because he is a perfect person or somehow earns it. That is his God given role in your home, and God commands you to treat him accordingly. This is not conditional in scripture. As believers we must do things differently from this world.
I am not saying that you must agree, or condone what he is doing. And, I am not saying that he shouldn't endure the consequences of his actions. I am saying that your ministry of wife, and mother, includes dealing with the snares that may entrap those around you that you love. Satan is a deceiver, and will attack this weakness for as long as your husband lives. It's a battle that Christ has one the victory over for him, and yet he must trust God by believing this. When he falls into this snare he must trust God to lead him. Troubles and trials are never a reason for a woman to take the lead. As wives, we must be submissive, and win our husbands over with our conduct. He is your flesh, and he above all others, should receive your mercy and forgiveness. Being a woman of grace, and trusting God in all situations, is a blessing for God, your family, and you. If he is placing you, or his children, in a dangerous situation...then, certainly you must remove yourself, and them, from it. However, trying to manipulate him with your emotions, or control him with your speech, and actions, is only going to succeed in belittling him, and making him feel less of a man...he will only aspire to worthlessness if that is what he feels.
May I encourage you to be prayerful, not to talk against him to others, encourage the children to honor him, honor him yourself, and let him know that you understand that he has a struggle, and that God can help him with it if the two of you trust Him together. What can you do to help, and let him know that you are one flesh with him, and will love and serve him through it? Could you ask him to protect you, and the children, by setting boundaries for himself? Could he outline a plan, and create the terms that will protect you, and even let you know at what point you would have permission to ask him to leave? Does he know that you are afraid of losing him, and that you need his protection and reassurance? Or can he only hear demands and conditions that you have set into place? Is he being respected when you speak of this matter? Allow him to protect his family, even from himself if he has to, by giving him that opportunity.
I think the children could learn a lot from seeing their mother honor God, and their father, in this situation. It is a trial, but God can make it a blessing. It can draw your husband's heart towards Him, and you.
You mentioned that you lost your first husband. I am so sorry for you and your children that you had to go through that. Your current husband is a blessing. Remember to treat him that way. Your heart, and the heart's of his children, belong to him. Do not let a trial turn them away...that is exactly what satan desires...that is his whole plan...to destroy your husband's family through this sin. Trust God, by trusting your husband, even though he is sinful. Show them both that you love them through your obedience. If you usurp your husbands authority, you disobey God and come out from under His protection.
http://www.aboverubies.org This site is very encouraging to wives. Click and then go to articles and stories section, then look under marriage. They will bless you. They also have a magazine, and it's free.
I hope and pray that you all come through this, and ultimately that God is glorified in it all...and that you, and your beautiful, family are delivered and blessed immensely. He has a way of using these things to make our lives more joyful than we ever thought.
Blessings.
Oh, I also wanted to mention that our church has a program called reformers unanimous...many churches do this program.
http://www.reformu.com You may find a location in a Bible believing church in your area. Maybe your husband will want to go one day.