By "doing Parelli" what resources are using to learn about it?
A couple of things you mentioned are addressed in Parelli very early on. Don't hide the halter. If your horse doesn't want to be haltered, and you want to use PNH methods to work with her, then you have other things to do first (namely sending her away from you which is counterintuitive I know, but it's about dominance and who can make who move).
The second thing they teach early on is that horses are used to being caught for work. One exercise is to simply spend time in your horse's environment (pasture, paddock, whatever) without asking them to "do" anything. No haltering, no brushing, no attention, nada. You let your horse initiate contact with you. You'll do this every so often, especially in the beginning because it breaks the cycle of "here she comes, I'm going to have to work again".
When you board your horse and have limited time like you do, you lose some opportunities to do this just in the natural course of horse care. I muck my horses' paddocks while they're in eating, I piddle around in the pastures fixing stuff or picking up branches, whatever.
It's going to take time to do this and it's going to take time to make her want to do this, but if this is the method of training you choose, please get the first series of DVD's (I think they have changed it up now, but it was the set of Level I DVD's when I got them) and watch them in their entirety first. Then, it's helpful to find a Parelli group in your area. Having a mentor, people who are further advanced, will be able to help guide you in their group play days.
The whole natural horsemanship thing isn't about loving a horse more than others, and it's not about loving them enough to will them to respect you, it's about communicating with your horse in a language they can understand, being respectful, but also getting respect from them.