If you're setting up a 2 day split, why not try something like:
I've tried something like this and stacked (superset?) the movements to get out of the gym quicker.
Another thing is to try the established programs that others have mentioned.
How I set mine up was (just as an idea for you)
Day A: Chest/Back/Bi
-Bench Press and Seated row super sets
-Incline bench and pullups or pulldowns
-Deads (superset with flyes if you want. I have a nagging shoulder so I only do 2 chest movements)
-Hammer curl and calf raises
-Barbell curl and ab work
Day B: Shoulder/Legs/Tris
-Military press and lunges
-Lateral raises and squats or hamstring curls
-Face pulls and hamstring work
-Pick a tri movement or two.
Something like that.
I think you're trying to do a little too much hitting back/shoulders/chest on the same day, but that's just been my experience trying things out in the gym.
Any reason you don't want to try a 3 day split if you can get into the gym 3x a week?