This horse has no respect for you, hence the rearing on the line and striking. Whether or not she is also exhibiting this in other areas, only you know, but make no mistake, you are not dominant over her at all. It may be that you have never had much dominance over any of the horses you have worked with, or it could be that they have been horses more easily intimidated, either is possible.
Be aware too, that with this particular horse, more than any other, any evidence you give that you are beneath her is duly noted and file away. Timidity in leading, haltering, grooming, or what have you will only add to this type of thing.
The feed she is getting, if grained/hayed could also be adding to this, and might need to be reassessed to see if that helps somewhat.
And am not quite sure if by "long-lining" you are trying to drive her from the ground, as to me that is long lining, or if you are lunging her in a circle. Under either circumstances, no horse should be close enough to you for them to consider striking, and are you that close?
Or is she just coming up to express her displeasure at what you are doing, and a safe distance away from you? Either way, she is in dire need of a come to Jesus meeting, and one in which there is no doubt in either of your minds who has won.
And does she really have any inkling as to what you are wanting her to do? How did you start her on it? When you say she is light on a ride? How much has she been ridden, if any?
IF she has been ridden and this is showing up there, you need to bring her down, the best and easiest way to do it is to pop her between ears with warm egg, and ignore her after that. She comes up, pop, down she goes, and you continue on. No talking about it, just go on about business.
I also would suggest thorough vet check/dental too first. But really feel it is your mechanics and this mare's mindset that is the problem here.
If she rears and strikes on lunge line, tear her rear up with 12 ft lash whip, or can use a cane pole. And I don't mean beat on her, but make it imperative that she go forward at your direction. Any display of displeasure on her part, results in another tap on rear.
Again, you need to evaluate your handling of this mare elsewhere, as rarely is one showing signs of this without it occurring at other times.
Horses make me a better person.