Sorry, I haven't had time to read all of the replies because only my opinion matters to me. Totally kidding but, here's my opinion any way...
FIRST of all, 2 very young children with 2 different guys?! Yowsers... and that's all I have to say about that.
Secondly, it is not your responsibility to be your sister's saviour, and even if you did help her out, it doesn't sound like she'd be very appreciative of it anyway. Just because you are her sibling doesn't mean you are obligated to help her out financially. I mean (going back to the first item, I guess that wasn't really all I had to say about that) maybe she should have thought things over a little before she fell into bed with her baby's daddies. Was she somehow wealthy when she had the first one, then decided to add another one to the mix and then suddenly lost all of her wealth? Really?! She didn't notice how expensive it was to take care of one child, so she decided to have another?! And why aren't the dads paying something toward these children?!
And cigarettes?! REALLY???!! Maybe she should think about scraping together the rent instead of buying smokes. And turn off the cell phone, turn off the cable, turn off everything that isn't a necessity! You can get a free phone that only dials 911 for emergencies. What would she do if she didn't have your mother or you to ask for the money? She'd have to give up the luxuries to pull money together. It sounds like her priorities are a bit skewwed.
Furthermore, shame on your mother for trying to guilt you into giving in to your sister. Your mom raised her children, it's time to cut the apron strings. Your sister is never going to learn to stand on her own two feet if she's standing on your mother's. I think you're going to have to face it though, that your mother isn't ready to let your sister hit bottom, even though she, herself, sounds like she is near the bottom. And I might get torched here, but shame on anyone on this board who bashes you for NOT giving your sister the money. This is a budget board, if you had money to be tossing around to other people, you wouldn't be asking "budget board friends" for advice.
Im sorry if I sounded like I attacked your family, but topics like this get me fired up! I pay taxes, therefore I support the misfortunate. But a lot of misfortunate people have a misplaced sense of entitlement where they think society owes them something. I don't owe you anything, Jack, get off your @ss and help yourself a little!