Having raced on a "touring" geometry front ends, I can tell you that such a bike is just as stable mid-turn but does not want to turn in quite as quickly.
First race I ever did I was off the back, my teammate yelled at me to corner like I was trying to fall over. I did, I didn't fall, and I went faster.
Do corners in the drops. If you aren't comfy in the drops (can't brake, shift, etc) then your bike is not set up right.
Weight the front of the bike.
Lean the bike and your body the same amount. There are reasons to lean one more than the other but for now, the same is better. This lets you get into a hard cornering "groove" where the bike is extremely stable while at a very hard cornering angle. Leaning bike or body more makes it a little less easy to get into that groove.
Inside pedal up, at least to start. Then start pedaling out of the turn sooner and sooner.
You can practice cornering lines at sub-25 mph speeds but to practice cornering where you actually "set" the bike at an angle, I think you have to go 28-30+ mph (entry speed). Remember, start on a clean dry surface. Then not clean but dry. Then wet but clean. Then wet and not clean.
Cornering lines, short discussion:
http://sprinterdellacasa.blogspot.co...ing-lines.html
Setting up bars and why you should set them up correctly:
http://sprinterdellacasa.blogspot.co...for-crits.html
Note how it's easy to shift and/or brake from the drops. If you can't corner from the drops, you're simply not weighting the front of the bike enough. Much easier to wash out the front wheel. Exception is if you do a LOT of long descents (i.e. 20-30 minutes or more, avg say 30-40 mph with switchbacks - for me that means 15 miles of descending non-stop). For short 1-2 mile descents, no need to have a slightly higher position.
Why setting up your bike for riding on the hoods may not be the best thing.
http://sprinterdellacasa.blogspot.co...hy-i-hate.html
Practice cornering on clean, dry pavement. Then progress to not so clean, not dry pavement. Don't do it like I did (as a kid) but you'll get the idea here:
http://sprinterdellacasa.blogspot.co...hen-youre.html
hope this helps,
cdr