I have never done a 3 day split that I remember, I have only ever trained upper/lower push/pull and full body.

My shoulders are only getting worse on 3x week training, and due to new restraints I must move on to a 3day split rather than a 2day split.
The only thing is I must do legs and back in the same workout, which doesnt leave much to split up into 2 days.
So it will be like:

Mon ???
Tue ???
Wed: Legs and Back
Thu ???
Fri ???
Sat Legs and back OR off
Sun Legs and back OR off

Bodyparts are:
Chest, triceps, side delts, rear delts.
Done 1x week: rotator cuff work, hip flexion and extension.

I use 2 exercises per body part, 2-3 sets per exercise.
My triceps get hit considerably when I train chest.