Maybe do some longing before you take off? That way you can see how she might behave, and thus can thwart it by working through it until she's focused on you; you will also not be in danger of being hurt should she decide to go up (and possibly over).
It does sound like she just didn't want to "go" away from home though, by the way you describe what she was doing. Lead, stop, act up, other horse gets ahead, then she goes foward okay (until she gets ahead, to which the pattern repeated itself). The fact that she lead fine going towards home, proves that she just didn't want to go away from there.
On the roads you ride on is there any space at all to put her to work? If so, then do so; try to avoid the backing, as rearing is not a good option, for either of you. If you have to, keep a halter and lead on her, get off quickly and put her to work immediately, and work her hard...going forward has to be easier than the work you will make her do if she doesn't; make sure the other horse actually stays where you want him on the ride (behind, or infront of her), but have them stop.
Allowing the other horse to get ahead, will only give her a reason to catch up, but won't guarentee that she will go forward once she does. You have to get her thinking that she has to go forward whether she is in front or behind, and if she doesn't do so undersaddle, you will make her move from the ground, but either way, she isn't being 'rewarded' by standing around, or trying to get away from you. Soon enough, she will figure out that going foward willingly is a much better option than getting worked hard.
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."