It sounds like your sister, due to her mental illness (hopefully she's getting treatment?) isn't capable of responsible money management. If possible, automating bill payments and limiting the amount of cash/credit she has available might prevent the overspending. But realistically, that may not be possible without a guardianship or something.
Giving her money directly, in any form, may be enabling. And since there's kids involved, that just makes things harder. A more comprehensive solution may be needed.