Mephala says that she cannot reach "your plane", but Sanguine seems to have no problem manifesting himself in Mundus. Is there a particular reason for this?

Maybe she chooses to stay shrouded in mystery. As for Sanguine, I think all the drinking, partying, and orgying mortals participate in allow him to pierce the veil of the Void easier.

There's some implication in the quest "The Whispering Door" that Mephala's ability to manifest in the mortal world has diminished. This could be the result of the inverse of a concept mentioned in the Seven fights of the Aldudagga, wherein Mehrunes Dagon is able to manifest in Tamriel due to the destruction of Sarthaal. In other words, Mephala's ability to manifest may be hindered by a lack of events that correlate with her sphere. Such a lack could have been caused by a combination of the Dark Brotherhood's diminishment, the likely destruction of the Morag Tong, and the decimation of Morrowind during the Red Year.

As for Sanguine, weak manifestations of a Prince aren't unheard of. We've seen sheogorath drop burning dogs, Azura appear before us a dunmer woman, and molag bal tossing pots. Sanguine appearing as a drinking buddy isn't an exceptional incident of Daedric meddling.