dips i feel are heavy on the chest for me, they are kind of like a decline press in a way, and shoulder press i always beleived is the best shoulder move by far, i thought compound>isolation is widely accepted as true, especially in strengh training, but i could easily be wrong.
so your suggesting squats day 1 and deadlifts day 2? that could work, i thought doing them both the same day gives me more time to recover inbetween lower body workouts