All your love, support and presence in the past has NOT changed anything for HIM, but caused your a lot of stress and grief. You have gone thru this without any support from him, until it has sent you for help and support from those who have had similar experiences and nightmares.
Thus it should be for him....he needs support and help from those who know what it is to be an alcoholic, and to have fought against that addiction.
His responsibility is to himself, his sobriety, recovery and program.
Your responsibility is to your wellbeing, sanity and health and mothering your children.
Mothering him is NOT your job.
As for buying a house and moving in together.......NOT now and maybe never.
This can be put on hold, until he demonstrates his commitment to sobriety, and you are satisfied it is what you wish to do. The dangers of doing this now are legion.
He is only a few steps along his hard journey, and has a long road ahead of him.
Use that time to get in touch with YOUR wants, dreams, needs and who you are and then you can look at this with clarity, and not thru the fog of dealing with an alcoholic.
God bless