Actually, it's just occurred to me: Are you simply piling on too much gas too soon instead of being patient and waiting for your moment?
In my experience the right moment to begin accelerating is just after you finish the lowest radius section of the corner. For instance on a hairpin, you would make a more L-shaped line through it, and would start accelerating just after the "crook" of the L and just before you hit the apex.
If you have a car that tends to drift understeer, you will need to take the apex at a deeper angle than you would with an oversteer car. For cars with ancient suspension like the Trans Am, it's important to not let the car roll too much. Keeping the front-outside suspension loaded is key. Taking a deeper angle at the apex will compensate for any drift understeer and allow you to accelerate more on the exit if you don't understeer. If you load the outside front suspension properly, it should feel like the car is gliding, and you won't have to correct your steering much.
Setup is also key. Having a brake balance set more to the rear will allow you to rub the brake under turn in and get that much more response out of the front wheels.
Also, on any car, if you take a corner too early but at the proper speed, everything will understeer. Before you try any thing different in the actual corner, try making the turn in later.
PS, on left-foot braking; don't. If you don't feel comfortable doing it, don't. You shouldn't ever need to use the brake at the same time as the throttle any way. The car only wants to do one thing at a time.
Ah, and final thing, if you haven't already, learn where your torque is! Especially for low-speed cornering. On most cars the torque builds with RPM, but not on all. For instance a Viper SRT-10 gets maximum torque at around 4.5k RPM, then falls off. It's very important to get the powerband right on exit and to tailor how much torque you get with your driving style. I don't like a lot of torque because I've very early on the throttle, but other drivers might like more.