I don't have an RS4 but the key thing in any onroad car is the alignment and suspension settings. These can only be accurately adjusted on a setup board and tweak station. For the setup, since you're just doing runs in a lot, get an RPM gauge at the very least to adjust toe and camber. Sway bars will help the car stay flatter in the corners but if the basics are off, they won't do anything but compound the problem.
A tweak station (for suspension settings via threaded shock bodies) will balance the suspension preload so that holeshots and handeling in the turns will be balanced.
All cars will slide out in a corner if there's too much speed and/or power applied. If you have a front oneway, you have to keep steady power in the turn to keep from swinging the rear aorund. If you have an open diff, you can coast intot the corners. Both have their pros and cons but it's all in personal preference.
The most important adjustment in cornering ability lies between your trigger finger and the brain. I learned this the hard way when I started racing competatively. Throttle control is the most important factor.