My husband's mare used to have this problem. Didn't have a "whoa". When you could get her to stop, it'd be a split second or two and she'd start to walk off again. He didn't do a lot of transitions to fix this...just one thing. And he fixed it in a day. He backed her up. It sounds like you've already tried this some, but then you say she starts refusing to back? What is she doing to refuse? We use backing a lot as a correction. Not only does it help build muscle, but it teaches them to soften their neck and collect.

If I were you, I'd spend some time with backing first. Practice backing until she does it softly. Of course, that's going to depend on your cues and release to get her doing it lightly. Our horses will back with nothing more than a shift of our seatbones.

Then, I'd ask for a stop. As soon as you ask and she doesn't, make her back. Let her stand for a second or two so she realizes that's right. If she starts to move...back her up. When she'll stand quietly, move off again...and repeat. If she gets stubborn with backing as a "correction," keep asking. Don't let her "win"...that's how she's gotten so resistant in the first place. With other people riding her, she's learned that if she ignores cues, she eventually gets what she wants.

I wouldn't switch to a harsher bit. If you keep your hands low when asking her to back, even if she's extremely resistant, you should be able to wait her out. The reason is that, if your hands are low so that her nose is being brought back to her chest (think extreme rolkur), her neck is going to get tired before you will...she'll want to back up to release the pressure. Then, of course, as soon as she backs up, give her the release.

I once joked that my mare could do an endurance competition *backwards*. LOL That's because she can be pretty hot-headed and stubborn...so there are a LOT of situations where she tries to evade, run off, refuse to stop, etc. She hates puddles, mud, logs, you name it. One time, I backed her all the up a hill because she didn't want to go up it (away from the barn). So fine...she got to watch the barn while working *harder* and still going the direction I wanted. I only had to back her up it the one time.