Hey there, welcome to the Community. There's currently no way of searching for alternate versions of albums on mobile devices like you can on desktop, but if you add the explicit version on desktop into a playlist that version will sync over to mobile.
This is also an issue for me. I really like Spotify but this is not an issue I had using Googles streaming service. I dont understand why it seems to default to the edited versions of albums that I listen to. My Android phone works fine so it's not the mobile side of it, just the ios side im guessing. Right now i just searched the artist name on my ipad and on my galaxy s4 and i get the edited version on my ipad only and both versions come up on my android. This is something that seems like an easy fix on your end. Would really be appreciated it.