i mean she must have also found out that sanji has been away from his family for the longest time after she searched for his past. she must know that he doesn't mean much to the vinsmokes but she still needed them to get near her and have this ceremony take place. all she needs to do now is trap them or take them hostage by taking away most of their life and forcing them to do what she wants. i wonder when we will get an update on zoro and the other strawhats. i want to know what happened to marco.
The numbers of tells they have in what can be generously called their con are so numerous that nothing will anger me more in this arc than if Big mom doesn't laugh in their faces when they try and pull the turnabout on her.
For one, Big mom is a pirate and they are willing to deal with pirates. Suspicion and distrust should be an automatic response.
Two, as Gaime mentioned, Big Mom has literal eyes and ears everywhere in her entire home that the vinsmokes blatantly ignore. There is no reason for her not to have a standing order to report suspicious shit.
Three, I don't have actual evidence of this, but I really fucking doubt that this will be the first time Judge has pulled duplicitous shit in his career as a warlord. You see that character and how he acts, and we're gonna assume he hasn't stabbed people in the back before? Nu-uh.
Four, there is no way that Big Mom won't see the transparent power play. "Oh, you want to bring my daughter to your kingdom without any of her own guard and have her stay there permanently? NOTHING SUSPICIOUS ABOUT THAT!" It's just so elementary, even someone without Big Mom's resources and natural piratey suspicions, you'd have to be remarkably naive to not be able to tell what Judge is trying to pull here.
Five, if Big mom has the resources to figure out that Sanji was with Zeff all these years, she has the resources to figure out the
public announcement judge made to his entire kingdom about his Sanji being dead from an accident and how that doesn't fit his story. We don't know how she gets her information, but if she's able to figure out Zeff, I feel like she should know everything like Sanji's history, Judge's actual reason why he left him, etc, but even if she can't get those, there is no way for her to miss public, on record announcements.
Honestly, I'm still unsure why she is bothering with these jokers. This could have just been a business arrangement at best or she could have just forcibly taken their technology at worst, since their so weak. I'm hoping she just likes fucking with them and is just waiting to pull a Red Wedding on their dumb asses.