Up to now, I haven't said a thing about Erika's personality... because she's just been a cipher, a woobie for the main cast to comfort. The dinner that evening (and the ensuing events) gives us a better idea of it, explaining how she fits nicely in the Ushiromiya household. Which is to say, she's a clever bastard like everyone else.
Wait, that didn't come right. Let's backtrack and elaborate.
Erika is completed unintimidated by the tense atmosphere inside Rokkenjima, or the high-class dinner she participates in. She's perfectly at home with the complex cutlery, for example. And then, seeing how tense this is making everybody, she breaks the mask (or does she ?) and starts babbling childish nonsense about the superiority of Japanese chopsticks, which livens up the mood and makes everyone relax. (This scene is described in Death Note-like detail, each casual line of dialogue underlined by the narration explaining the subtext and machinations of its author. In particular, Hideyoshi appears as a master of ice-breaking and Obfuscating Stupidity.)
Interestingly, for once the dinner does not go straight to the familial conference, as the lighter mood incites everyone to have a break. On the way to the guest house, Erika notices Beatrice's portrait, and the discussion shifts to the mysterious epitaph. Apparently, she delights in this kind of intellectual puzzle, and becomes much more talkative as she reaches her first conclusion : the epitaph is Grampa's sign that he does not want his succession to be simple for Krauss. He intends to make the solver of the riddle his full successor.
This is not really news for anyone, but having an outsider say it brings to the open what were only hopeful conjectures for most of them. And it really displeases Jessica, who does not like her father's status challenged, and has taken a strong dislike towards the newcomer (I presume that Natsuhi and Krauss are busy elsewhere, because we're not shown any reaction or presence from them). Thankfully, George prevents this from degenerating by shifting the conversation to the riddle itself. And Erika proposes to solve it with everyone...
Meanwhile, back outside the chessboard, Bernkastel announces she's achieved what Battler never could : solving the epitaph riddle.
Ah, now this is getting even more interesting. Our first peek into Erika's character shows that she's a bit of a prick (she can't ignore that she's winding up Jessica, but still continues doing it), and we're promised a solution to the riddle right now, before any murder even occurs. (And remember, this is more or less a flashback : Bernkastel and Lambdadelta reenact the beginning of their game for Battler's benefit, so all of this has already happened for sure.)
So far, Erika's bitchiness has been quite restrained (I'm treating her as a separate character from Bernkastel, who makes a point to be gratuitously nasty at least once per scene). She displayed some surprising tact in the dinner scene, and up to now she's only been provoking Jessica for no obvious reason. (I notice that Jessica is one of the first victims, and thus Erika doesn't need her cooperation to play detective later on. Hum...)
I'm sure she'll get worse, but let's not forget that she needs the cooperation of most of the others in order to do her detective work. So she can't ruffle too many feathers... (On the other hand, her profile in the TIPS indicate that she'll magically get the authority to wave accusations around because she's the detective.)
