Basically, you've got a coordination problem between power and control, and the guys above touched on parts of it but didn't nail it. The support foot does matter, but the real culprit when you want to shoot hard is that you're accelerating the movement before your body is aligned. Your body tries to put in more energy and automatically destabilizes, so the ball ends up flying off in any direction. The ankle tension that someone mentioned above also plays a role, but it's a symptom, not the cause.
What I'd recommend is breaking this into two training phases. First work on shots at half power for two weeks, making sure every single one goes exactly where you're looking - not a single one off target. Keep in mind you're not being slow here, you're being precise. While you're doing this, work on the stability of your support foot: when you strike, that foot has to be fixed and just slightly ahead of the ball, like an anchor point. Then gradually ramp up the intensity, but keep the form.
Once you nail that, hard shots are going to come naturally because your body's going to have the right structure before you put power into it. What's probably happening now is that three training sessions a week help you out, but if you're reinforcing the wrong movement, you're progressing really slowly. Better to train fewer times a week if you're actually going over technique in each session.