ok, answering your question, most people take protein powders immediately post workout, because the body needs nutrients, esp. protein and simple carbs, right after a hard workout.
But again, 2 workouts a day is madness. You're gonna slip into overtraining within an extremely short time frame, and no matter how often you take protein your body will still suffer, make no gains, and likely fall prone to an injury of some sort.
pro athletes and pro bodybuilders with YEARS of hardcore training under their belts can pull off two-a-day workouts.
I don't believe you fall into that category. I know I don't.