Gosh,i really feel for you what an awful situation.
She absolutely is an alcoholic – the hiding alcohol and the defensive behaviour says it all also her family history they do say it can be genetic..
You are not misreading the situation – alcoholism is a disease and usually incurable, its so heartbreaking.. they usually dont seek help until they hit rock bottom, she needs to get to the GP and get help asap.
Unless she wants help, there is literally nothing you can do. You can’t force her, until an addict wants to get help then it will continue.
The thing that complicates this is your baby, she will know she needs help but until she really wants it this will continue, it happened to me and my partner, it took months of screaming arguments and then he got found on a park bench suicidal and finally he gave in and got help.
I wish there was a straight forward answer.. I wish you all the luck with this, its so heartbreaking. We are always here for a chat if you need it x