Have you consulted an attorney about a legal separation with financial support for you and your children?
The history of your marriage is that your husband is an alcoholic, has been so for at least ten years, which forced you to separate from him for the good of yourself and your children. When you did that you had to go into the work force to survive.
After a two year separation, he got sober for 6 months and you allowed him to move back in. You lost your full time job three months ago and now have only part-time work. And now he wants to leave you. Is all that accurate?
I would consult an attorney as soon as possible. Your husband is going to start drinking again, is my bet. You need legal protections all over the place when that chaos starts.
I know your money is limited but if you have medical insurance, please see your family doctor, tell the doctor about the alcoholism, and see whether insurance will cover some counseling for you and your children. All of you really need it. Families of alcoholics have tremendous pain inside. Don't let your children's smiles fool you otherwise.
Six months dry is but a whisper of sobriety. And without a program, your AH is just white-knuckling. He is on his way to a drink. When he picks up again, things will be very bad. You need to see an attorney and talk about legal separation and protections.
Your husband is sick with addiction. His behavior, in my opinion, and his desire to move out has nothing to do with you, the marriage, or with love. He is sick. He apparently has no recovery program. On his own, the cards are stacked again him getting sober not only physically but mentally and spiritually.
As much as you hurt, I hope you can come to a place of acceptance that his brain is damaged and he is not capable of being your husband right now. Addiction is so deadly serious. Kisses and hugs and dancing will not be the answer.
We are here to support you. But I also suggest you sit in an Al-Anon meeting twice to three times a week if possible. It is much too devastating to handle this all alone. Your thinking will be distorted. Your spirit will turn gray. You need to get yourself some help. You deserve to find your life force again. And your children need a healthy parent.