I doubt Yukari and Yuyuko are sisters, partially because I think Yukari is waaaaayyyyy older than Yuyuko(also, it would make very little sense, actually). She also predates the creation of Gensokyo by a lot but I doubt the Hakurei people could've done it without her help. Being arrogant and "almighty" as Yukari is, I think she'd change her name just for the sake of having it symbolise her own power and will, as opposed to heritage from a possibly forgotten family. The name itself carries HER legacy now (and is passed unto Ran, for instance).
I also doubt Yukari is one to "watch over the world and ensure peace". She's pretty much a fickle and irresponsibly wench who happens to have unreasonable amounts of power. It's clear how "responsible and watchful" she is straight from her appearance on PCB.
Yuyuko suddenly decides she wants to make the Saigyou Ayakashi bloom and asks Yukari to help her. Yukari knows the shitstorm is gonna be epic, but pretty much all she does is ask "You sure?" "Yeah, I'm sure. Can you help me?" "Hm, okay." And sorta just like that she almost erases the barrier between Hakugyokurou and Gensokyou so can Youmu can go and steal all the spring. The thing ends and Yukari wasn't even there to see what was going to happen in the end. Something like a month later yuyuko goes after Reimu and Marisa (by this time I guess Sakuya's involvement on the matter has probably ended) and tells them that Yukari fucked up the boundary but that now she needed it back up again unless things started turning BAAAAADDD on everyone. The problem was that Yukari never showed up and Yuyuko couldn't reach her. So M&R go and find Ran, that wants revenge for the two of them beating up Chen. They defeat Ran expecting Yukari to pop out and go defend her servant but nothing happens. "Hmm.. You're like in danger of dying here. Where the hell's your master?" "She's sleeping..." "Sleeping?" "Yeah... And it'll take more than this to get her out of bed this early... If you want to see her, you better come in the dead of the night, she MIGHT be awake then".
And so Marisa and Reimu DO come back in the dead of the night and fend off Ran again. Yukari finally shows up and, being bored to tears as she is, decides to throw some danmaku at the two heroines and see what comes out of it. They manage to defend against her and then Yukari asks: "Yay, so, what you two doing here anyway?" "Well, Yuyuko says you've got to fix the border now or shit's gonna get nasty." "Ah, she's done with that tree then? Good. Okay then, I'll fix it."
JUST LIKE THAT!
So, yeah, watches over the world and completely is not just trying to troll everyone.
Gensokyou is pretty much lucky she doesn't want to cause havoc. If she wanted to tear down the boundary between the living and the dead, open up the gates of hell (and even Makai, for that reason) and collapse the Hakurei Border, there wouldn't be anyone capable of stopping her, at least not until the damage was irreversible. The way I see it the only reason she protects Gensokyou is because is a nice place and her friends like to live there.