A pushy and reactive horse would run over the top of you if you sent them forward like that with a crop and then kept their front end pointed right at yourself. Your horse is very politely letting you stay right up in her personal space while you are cracking a whip. She even rears up and avoids hitting you. That is being very non-pushy.
Near the beginning of the first video, you send your horse toward the left side of the screen but you're not watching her. She hits the end of the lead, which pulls her face back toward yourself. Then you yank around on the lead and correct her. Why? She was following the lead rope.
It seems that the horse would benefit from more talking and less yelling.
If it feels like she is shouting at you, that is because you are shouting at her. Why can't you try a gentle pull, then a light tug if there is no response instead of every movement of the lead being a quick, hard jerk?
Also, how does your horse know what you are asking? Do you want her to move her hind end away from the whip around you once in a circle? Then instead of starting with six circles before giving a break and reward, try two steps. Then slowly progress up to one circle, and etc.
It might seem like she is pushing into you, but you are not giving her enough space to do anything except come into your body. A horse has a large body to move around.
If a horse reacts too quickly, slow down your own movements and cues.