Firstly, to OP, I edited some paragraph breaks in to your posts. Could you please try to include them in future? May seem pedantic to some, but some of us have a hard time reading big blocks of text!
I suspected early on that this horse has been desensitized to a whip a little too much. But anyways, I can tap tap tap all day on her hind end, increasing pressure more and more with no response until I crack the whip
Maybe in the past she's had some desensitising too, but agree with Tiny, the above sounds like what you are doing is desensitising too. If you tap at her(or whatever) and it is not effective, it will annoy her, but she can just put up with it until it stops - or you do something more effective.
Assuming everything is clear to her, she's not acting in confusion or fear, this is the kind of situation I'd say 'up the ante' a lot quicker. Absolutely start small, but give her ONE chance to respond to that before making it uncomfortable for her. Then ONE chance to respond to THAT level before cracking her a good one, and getting after her even stronger if required.
When this horse starts kicking out at me, I crack her across the butt with the whip, this can continue for a good 10 seconds, she kicks, I whip, then she turns on me like she's going to charge so I crack her across the chest, she DOES NOT back down like every other horse I've had to get after. I'm not afraid to use a whip when it becomes a safety issue for me.
Today when I got her across the chest when she was about to come at me she reared and struck out at me. The whip does not work with her. I dropped the whip, got after her by making her move her feet the only way I can. Yielding haunches, shoulders,
I am very concerned about this, that it IS not only a serious safety issue to you, but to whoever else deals with her. I am not one to use much force & punishment as a rule, but if a horse is actually threatening me - generally well before they *escalate* to charging & rearing - they are going to get WHAT FOR! With whatever force it takes to make them highly unlikely to want to challenge me again.
What it sounds like is going on here is a bit of a 'dominance game'. She's willing to back up her 'I don't wanna' with 'You & who's army?' followed closely by 'I've had enough of you - now I'll really give you What For!' Have you seen horses 'play fight' in the paddock? One will bite & the other one will bite straight back, and this can go on, tit for tat, then if the dominant one has enough of that, they will then drive the other horse off. Unless the one being charged objects, & then a real fight might happen. Sounds like that's what she's doing with you. And it seems that you are playing the game, encouraging her. Then when she does charge or rear, you drop the whip and do something she clearly doesn't mind doing(for now at least, tho she's learning how to deal with you on things she doesn't want to do, so...).
She is obviously a more 'dominant'(for want of better term) horse than you have dealt with. I'd been training horses successfully for many years, no real issue, before I came across my first 'shut down' one & came to realise I just didn't have the skills to deal with him without help - no harm in realising & admitting your limitations, but with a horse like this girl, who's clearly willing & has learned that charging at people is effective, I can see a lot of potential harm in giving her any more 'practice' at these lessons. If it were me, I'd be telling the owner that I felt the horse needed someone more experienced with her personality & call it a day.