Would Marie's blabbing earn attention of any sort that would help in terms of trying to dig out answers? If Marie is calling Dany over to tell the other ladies stories, Dany would try to press them for gossip in return. Make it seem like innocent jabber, then try to dig around about things that Marie might've hinted at. She'd also make a comment about the strange man milling about, the locksmith, and ask about him in more detail (and why they think he might be acting strangely).

While cleaning and dusting Marie's rooms, would there be anything lying about that Dany would notice? Maybe something pertaining to this secret about her husband or anything that COST would find of interest?

As for the secret, Dany would likely keep pressing, but make it sound like innocent fun by smiling, laughing, doing whatever she can to keep Marie at ease. She'd offer a secret of her own if a trade would interest her grace. It might disarm Marie enough or convince her that she has leverage on Dany, then... so why not share?

(Likely, the secret would be her admitting to flirtations with Jon, since she's likely been caught around with him and has been teased, as well.)