Crack Along Edge of Shower

[Clinton Holmes]

Hello BP Do It Yourselfers! 

The shower wall in one of my rental units has started to separate from the wall. See photos below (note they should be rotated 90 clockwise). How would you recommend I fix this? 

I was thinking about filling with composite sheet rock, waiting for it to dry, and re-sealing with latex caulk 

OR

Filling the crap out of it with Gorilla glue, waiting for it to dry, and then re-sealing with latex caulk. 

Do either of those sound like a good idea? 

Thanks in advance for the help!

Clinton