When you desensitize a horse to a stick or rope, you always want to follow up with them yielding to it. Desensitizing a horse isn't about showing a horse that the rope or whip is something to ignore. It's about showing a horse that it can be ignored sometimes, only when you're swinging the rope and whip about and you're not giving the horse any cues. It's just like your hand. Your hand is meaningless when you're scratching your hair, or swatting a fly away, or taking a drink. But it does mean something to the horse when you point, or swing towards their hindquarters, or pet them. That's exactly how the rope and whip should be. So after you show the horse that it won't hurt the horse, always follow up with asking them to yield to it just so the horse can distinguish when to yield and when to not care. Otherwise, you're going to wind up with a horse that ignores the whip and rope all the time, and therefore by extension, is going to ignore you all the time.
Controlling a horse's body is about influencing her mind, not her body. If you try to push your horse around, you're going to lose. She's either going to completely ignore you, or (as she has shown) get really irritated and start to kick or bite because it's extremely disrespectful to her. Think about if you walked up to a person and just tried to shove them out of your way instead of asking them to move over. If the person is a jerk, they'd say "uhh, no you don't," and probably punch you in the face.
Cues should be taught in stages. If you want your horse to move over, you should be able to do it just by tapping the whip in the air. If the horse doesn't move, then you tap the horse's hip. If the horse still didn't move, you'd tap it a little bit harder until it annoys the horse so much that the horse finally decides to move over. You always start with the lightest cue first, because the horse will know that if she doesn't move over at that point, more annoying cues are going to follow. Pushing and shoving the horse is only going to be met with resistance, and if the horse decides to plant her feet against your pushing and shoving, then the next highest cue would be kicking and punching, because that's how high you've set the lightest cue.