ML, who knows why he was so keen on a baby? My first instinctive thought was that he thought it would 'save' him by being so important to him that he wouldn't want to drink. This forum is full of stories where that belief is shown to be nonsense. Alcoholism is a hard addiction to break, really hard, often requiring a lifetime's work. I write as a sober woman who tried for to stop drinking for years before I was lucky enough to find the key.
Now you've had some time to yourself you're realising he's been living a secret life away from you for years. Do you really want this man in your house with your young baby?
You haven't said how you're coping with early motherhood? Have the events of the last few months affected your relationship with your daughter? I understand how the stress of life can stop you fully enjoying your lovely child as it happened to me. I hope you have lots of support around you from family and friends.
Now might be the time to seek legal advice and any other support you feel you need to tidy up your separation. You will need to quarantine as much money as you can for your everyday expenses and make plans for the future. There are lots of stories and resources on this website, as well as information from other sources.
In a way its lucky he's shown what he is this early. There's a beautiful life ahead of you without having to cope with an A in your daily life.