I think you've come to where you have to take a deep breath, and get FIRM. You KNOW you're too soft. A horse doesn't think "soft"-- she thinks, "I'd better take the lead, because someone has to." My little one is just like yours, an angel when at home-- but what I realize is, she doesn't keep all her attention on me, she always has an ear cocked on The World.
My first and foremost goal: Get Her Attention. Keep that in your mind. Do whatever it takes, and don't think you're being "mean". I start with leading at a walk, then I take off running, and if she doesn't follow right away, I smack her with the rope (okay, I also smacked myself the first few times-- not too coordinated) but I HAD to get her looking at me (at first wondering why I was hitting myself and laughing) and ONLY ME. It only took a few minutes. She thought it was pretty much fun, running and stopping and changing directions etc, all very sudden. As soon as her attention wandered, I'd take off, or jerk her around. You can't afford to be soft or subtle with this type of confident horse, I don't think.
One more note: when you start riding, even if she's perfect to lead, your "troubles" are not over. You obviously have a smart, take-control horse. Enjoy the journey of growing up with her, but don't expect it to be TOO smooth. But I think when she does learn her tasks, she will work her heart out for you.