It sounds to me like you just don't trust her at all. She's not wanting to get to know you at all, plus the apparent desire for secrecy on their part, plus her current desire to relegate relations with him to that of casual sex only. I can't say as I find anything wrong with being suspicious of her.
As for the last, is your husband interested in just an open marriage instead of poly relationships? If he's up for the casual sex instead of a romance, then it's a case of whether you're up for an open relationship in that fashion--and based on what you've said here, I suspect not.
Or is she wanting a romance with him that is open so she can have casual sex with others? That situation will require a bit more negotiation, I think.
When speaking of various forms of non-monogamy...it ain't poly if you're just fucking around.
While polyamory, open relationships, and swinging are all distinctly different approaches to non-monogamy, they are not mutually exlusive. Folks can, and some do, engage in more than one of them at a time--and it's all good.