L.C.
Honestly, I'd have suggested the women's shelter, even if you hadn't mentioned it.
The services and understanding they can provide will be of far more value than any 'kick her out to cope on her own' or handouts you could give.
What I don't understand, 'cause I'm pretty thick sometimes, is how she and her daughter were living with an unemployed person and now can't live on their own *without* said unemployed lout.
Of course, I'm a bit dense, and I've never figured out how anyone could stop me from having my own key to my own house, because have a phone book and can call a locksmith, take the key when the troll is sleeping and get a replica cut or even replace the locks myself... where do people learn such helplessness?
Jackie Chan, eh? Very cool!
Anyhow, what your sister needs is your calm reassurance, probably over and over again, that she's fully capable of finding and using the services available to her, and as an employed person, of finding accommodation that meet her needs, without you doing any of the legwork for her. She doesn't believe she can do it, but she can and she'll only find that out by doing it.