what I do, and I could be terribly wrong but it works for me 1) your statement is correct braking and turning, cannot happen at the same time. I downshift, to bleed out most of my speed and use the brakes for fine tuning, but either way, whether you brake then downshift, or downshift then brake you have to break the age old video game tradition of going into a corner way too hot and braking/sliding your way out, when a turn comes, you need to have already done everything in anticipation of that turn, from setting up your positioning on your preferred race line, to bleeding out any speed you dont want.
what you describe sounds a lot like what my brother, my brother in law and I kept doing when we started playing the game, we were seasoned racers from consoles mostly and it sounds to me like you are approaching on the inside of the corner, slamming on the brakes and trying to fishtail it (i could be wrong) instead cutting straight across, its a tactic that works in a lot of games on a lot of systems and has created terrible habits at least for us three. I have caught up a little quicker then my partners in crime (the setup is mine, unfair advantage) but I keep pushing them, the slower you look, the faster you are going, my current goal is to not scrub the tires, the less of it I hear the better.
Whoa I ramble too much, short verson, slowdown before the corner, and the second you are far enough into the corner to see a straight shot out, start to accelerate out. please if I am off base, someone correct me