Suspicious? Why? She's a single young woman of marriagable age and a celebrity, so she gets propositioned. Her mother said that she usually just declines the invitations. While it's in poor taste to rely purely on status to get a foot in the door, it's not unexpected that someone like that would still want to try his luck. In any case, her family would be the first to get suspicious if there really was cause, not an outsider with no idea about noble society, like Youki. Given their relationship with him, they'd ask for his help themselves.
As for "traps", while I can't rule out some strange deus ex machina for that to happen, in the end that would just be bad writing. Logically there is nothing to blackmail her with and no real way to strongarm her, without drawing the ire of her friends and possibly the kingdom itself. The other hero was an asshat with a superiority complex, and he did talk tough, but didn't attack her in the end, likely for the above reasons, since he had no trouble attacking the peasant girl.
That's the thing, the whole "turning of tides" is the wrong way to approach this. Rather than thinking what you could do to make some impossible comeback, you should think about what got you to this point in the first place. A relationship based on some great turning moments, rather than the natural, everyday buildup of affection is a sitcom thing that will likely end in yet another grand spectacle. This is the reason that the MC's and FMC's interactions seem genuine and promising, unlike the shenanigans of many shounen manga, where pointless drama is king.
