I understand not being able to play 2 cloud songs on one Apple music account, but why can't I play a song/album I OWN (bought from iTunes) while playing another cloud song on Apple music?
What you are asking for can be far more complex. What if you have a Playlist and ever other track is one you own and an Music track. Should it stop playing on the other device and then start back when you start playing an owned track?
You should absolutely be able to do this. Verify the owned tracks are downloaded locally and try again and avoid mixing your tracks and Apple Music tracks in the same play queue.