OK. There's an "A" plot and a "B" plot going on here, albeit with some added complications thrown in.
The "A" Plot is pretty straightforward: 'Odo and Dax investigate a strange discovery on a planet in the Gamma quadrant'. For plot explanation purposes, that's pretty much all we need to say about them. Unlike other episodes, there's no interaction with the "B" plot, other than to explain Odo's absence from the station.
The "B" Plot is best described as 'Major Kira is covering for Odo while he's off being part of the "A" Plot with Dax":
In typical fashion, Quark is attempting to arrange a meeting with his cousin Kono to fence some stolen goods. He's aware that Odo would prevent this and has waited until he left the station but Kira catches wise to this, intercepting Kono at the airlock who promptly beams off the station.
In an attempt to distract her (to allow a further attempt to receive the artifacts) Quark uses his influence with Prylar Rhit to convince him to invite Vedek Bareil to the station, in the hopes that he and Kira will give in to their throbbing biological urges and forget about him.
The bit that you seem to have missed is how Kira suddenly pieces together why Bareil is on the station;
BAREIL: You better tell him soon. Prylar Rhit is going to be returning to Bajor.
(off Kira's look)
It appears he fancies himself something of a Dabo player.
Kira is beginning to get a nasty suspicion.
KIRA: Let me get this straight. The man who invited you to the station, owes money... to Quark - DS9 Script: Shadowplay
Oh, and there's also a tiny "C" plot chucked into the mix, basically setting up Jake's decision to refuse a career in Starfleet. This is largely irrelevant to the two main plotlines.