He is not the role model that you want for your children. The only thing I can suggest is for you to leave him if he doesn't seek professional help and recommit his life to you and your children. He made need to get worse before he realizes he needs to get better. you need to protect your children more than you need to protect him.
It sounds like he may really want to change, but he lacks the willpower and support. It is not that you don't support him, but he needs the support of a sober individual that can relate to his own experience. Someone he can call up when he is down and will remind him that his choices carry responsibilities and consequences.
He can go for long periods of time sober, but is unable to quiet the addiction within him. Ask him to go to AA or NA. You may also find comfort in a support group like Al-Anon.
Best Wishes and I am so sorry you are going through this!
Sorry if this is garbled. i haven't woken up yet and my proofreading skills are sorely lacking. I will gladly clarify what I wrote if it is unclear.