Wow congrats on the new family member though its not under the best circumstances its a blessing in its own and that your daughter isnt drinking.
Regardless if your daughter has the baby, alcoholics who want to drink would not care and still drink with young children so perhapse its better that someone else tend for baby or atleast help with baby being vigilant.
Im not sure as far as her living arrangements and public assistance however...perhapse thats something to look into with where you are.
Once there is an innocent child involved I think the " her" problem becomes reasonably unimportant. ...as this is your grandchild. Im assuming she is a first time mother in which case her statement that shes been looking for a job (you of which dont believe is in much effort on her part)
Could be nervousness and anxiety on her part as a new mother and recovering alcoholic.
I can understand your other daughter not wanting her around her child....but maybe that can be resolved. At some point between sisters as she remains sober mending the trust she had broken.
Best luck