First, thank you Lillym! I just got back from a family camping trip with a couple of difficult individuals, and my tongue has bite marks as well. :)
Really, I just chalk it up to that person just being 'them'. Let's face it, in your situation, your sister isn't really wanting advice, she's just being self-indulgent and wants sympathy for making poor choices, at least from outside perspectives. (Maybe she has some strange biological need for Coach and Tiffany that most of us aren't afflicted with.... aren't we the lucky ones?! ;) )
Seriously, though, there was a time this weekend when someone was insistent that their recollection of something ( a very small something) was correct and wouldn't let it go... they kept on and on and ON talking about it. I just chalk it up to 'wow, okay, you're crazytown about this today, so I'm just going to smile and say nothing and you can think what you want and I know the truth'. Instead of arguing about it, frankly, I did just bite my tongue and practiced the 'active ignoring' like I do with my son-- listening for that person to get off their rant and move on to more pleasant topics of conversation. It keeps the peace without either validating or confronting a person whose behaviors I am never going to change.
People will change when they choose to, when they want to, when they realize that what they are doing somehow isn't working for them. I can have compassion for that person because I know their memory is slipping and this is something that they may be highly defensive about-- sometimes a person's conversation is more about reassuring themselves than about being combative, it just may come across that way.
As for the imposing on family members thing, make your own boundaries and only take your sister's kids when it works for your family. There's no reason to feel obligated if she's really capable of getting childcare and is mismanaging her money. And as for the others who are willing to facilitate her 'user' behavior... that's for them to grow a backbone and deal with.
Oh, and a couple of "I'm listening" neutral phrases I like:
"hmmm"
"well, isn't that something"
"guess that's just how it is"
Acknowledges that you are listening without committing to any opinion.