You need to forget the calm and trusting part. Concentrate on horse handling skills, which means horse needs to respect you.
If horse is balking while being led, more than likely it is because you are not leading her correctly, and she has learned that once she plants feet? You can't make her move.
First off, lead her with your shoulder at throatlatch, right hand close to snap of lead rope, but your body needs to be elbow length away. This gives you an easy correction if horse surges ahead, or lags behind.
When horse plants feet? Don't look at her, but move her head and body to one side and then the other to untrack her body and force her to move. Once she does, go to where you were heading.
Also, find someone who manages their handling of their horses well, and watch them, and if you can, ask them to help you. And not someone that babies horses, but someone with good skills and common sense. Those are the people that you can learn from.
If you have been babying and loving on this horse, quit it. It is not a kitten or puppy. The more it thinks it can boss you around? The more it will, especially as it already has learned it can get by with it, hence the warning about it not wanting to leave barn.
Take some lessons too, if you can. Much of what you will need to learn about horse handling, is so much easier if it is done in person.
Horses make me a better person.