I have two albums from two separate artists with the same name (the album)

Solo by Michel Camilo
Solo by Luis Julio Toro

And they have been misidentified as a single album from various artists. Is there a way to force amarok to realize they are two separa albums?

You can batch rename one of the albums (retag the audio files) with a tool like Easytag. If it's not in your distribution's repository, you can get it here.

Like macemoneta implied, the problem is likely not with Amarok, but with faulty metadata of the audio files (ID3 information of your mp3 files). You will need to change the metadata in order to get Amarok to handle the files correctly. EasyTAG is one of the tools you can use for this, but you have other choices too (ExFalso, Kid3, and many many others). I think it can even be done in Amarok itself, but as I don't use it myself I really don't know how.

Notice also that there are two versions of ID3, the older 1.x and newer ID3v2. The older version is really limited, so my suggestion would be to use version 2.

ogg files I made by hand.

Ogg files have tags too.