Groundwork for respect?

You need to let her know that the cutting in is unacceptable. Take the end of the longeline and smack the horse's shoulder with it. Make a negative noise, like NO. You are already doing groundwork when you are longeing. Just be firm when you tell your mare that you have a bubble and she can't pop it. An alpha mare would bite and kick at the offending bubble popper, and you need to do the same. Smack, yell, and make it uncomfortable for your mare to be in your space.