1999 Toyota Corolla Brake system or tranny?

This sounds like you're trying to describe a dragging brake that isn't releasing. A sticking brake caliper is a good guess, but there's a more likely suspect. That's the rubber flex hose attached to it. The way to find this is to get it to act up again, then stop on a slight incline, shift to neutral, place a block about a foot downhill of one tire so you won't look funny chasing after your car, then loosen the steel lines at the master cylinder. You'll need line wrench for that, also called a "flare nut wrench". A regular open end wrench will usually round off the soft metal line nuts.

If loosening the lines there lets the brake release, we'll have to talk. That can be a very expensive repair. It's more likely the brake won't release there, so tighten them back up.

Next, open the bleeder screw on the caliper. Most likely the brake will release proving there's brake fluid trapped there under pressure. There's a metal bracket in the middle of the rubber flex hose where rust can form and constrict the hose. You can force brake fluid through it with foot pressure to apply the brake, but there's no pressure to make the fluid return to the reservoir, so it stays there and keeps that brake applied. A shaking in the steering wheel is a common symptom of a sticking brake.

I've never replaced an ABS hydraulic controller for blocking brake fluid return, but that can be verified the same way. Loosen the steel line going to the locking brake. If the brake releases, the controller could indeed be the cause of the problem.