But also when Kermit wishes he'd never been born he sees a Doc Hopper FrogLeg store
AVMMC, just like any muppet movie, is it's own thing. For one, it seems that "The Muppet Show" doesn't really exist in that continuity, at least not as a tv show. It seems to exist as just a stage show with no cameras. Also it seems that the muppets aren't exactly famous in that special, or at least not to the extent that they were in "The Muppets". The Doc Hopper thing is a reference to TMM, but that doesn't mean the two movies follow each other exactly.
To me, AVMMC seems to be an extension of the events of TMS, but not an extention of the "real" muppets. It's an alternate universe in which the muppets did a stage show, and nothing else, and have been doing their stage show for some time now. The Muppets seems to be an alternate reality in which the muppets met in a manor similar to the events of TMM, did a TV show called the muppet show, which led to TMM, GMC, and MTM, but their careers ended in the late 80's (meaning the MCC, MTI, MFS, and any other post Jim Henson project doesn't exist in this reality).
In both movies the muppets are actors in a movie playing themselves. Neither movie is "real" or "history" which is why both can exist.
As for the confusion about the Kermit and Piggy being married thing, it seems that the marriage scene in MTM was real. Now, by that I mean the scene was part of the play within the movie, but the real Piggy got a real minister to play the part of the minister in the play within the movie. It's confusing, but not if you rename Kermit and Piggy's characters in the movie. For example, let's put an A at the end of the characters in the movie. So, KErmit plays Kermit A in MTM and Piggy plays Piggy A in MTM. Kermit A and Piggy A are the leads in the play. In the play, Kermit A and Piggy A are getting married. But, during the scene Kermit turns to Piggy (outside of the movie) and says "I thought Gonzo was going to play the minister". Piggy laughs, and they continue with the scene in the movie. Now, the scene in the movie is Kermit A and Piggy A getting married, but since it is a real minister Kermit and Piggy (the actors making a movie, not a play) end up actually getting married.
So....the "real" Kermit was tricked into getting married by the "real" Piggy while making the movie Muppets Take Manhattan because they filmed a scene in the movie in which the characters get married during a play. In The Muppets, we see that they were in fact married, but then separated because Kermit was upset that he was tricked into marriage during the making of a movie. To me, this is perfect because it explains how they went from being married as characters in the late 80's to all of a sudden being indifferent to each other after Jim Henson's death in the 90's. Of the course, The Muppets is still just a movie in and of itself, but just like all of the movies, it seems the Kermit and Piggy relationship bits remain true (ie, Kermit and Piggy the actors fighting in GMC).