So, I'm going to ask a tough question here. What role does your Knight class fill that a Fighter or Paladin doesn't fill? There are some cool ideas here, but they ultimately only replicate what other martial classes already do. I like where you went with the sub classes, as that's what sprung to mind to me. Going Sword, Sheild and Mounted Combat with the sub classes just feels natural and fits.
Though when I read through this, I found that the features were essentially a pre-selected fighter or paladin build. In actuality, an Oath of the Crown Paladin is far more effective as a Knight as you've described in your homebrew. With Oath of the Crown, you get the challenge ability, resistances, a bodyguard feature that lets you soak damage for an ally, and ways to deal with hoards. So a Crown paladin can wade into a sea of combatants, call out the big bad and protect his friends. In addition, they have the paladin base, which gives them a choice of martial fighting styles, which includes protection if they want it. Really, it's the players choice, versus the class just choosing one for them. Then add in that Paladins get Compelled Duel anyway, plus lots of other spells. A paladin wanting to focus on mounted combat can summon a magical mount whenever they want. Some Knight class features can be replicated with feats. Great Cleave is essentially GWM without the GW requirement. Which is ok, but not enough of a standout to make me choose Knight over Paladin, considering everything else in the paladin package.
So what niche are you looking to fill with your Knight class? It seems to me that what you've presented is already covered. The fantasy knight or knight from legend is supposed to be represented in the paladin class. The martial soldier or non magical knight is easily represented in the Fighter. A Fighter with the Sentinel feat can essentially do the same thing as a Knight with their challenge, lock down an enemy. Plus the Fighter can do it without requiring a save. Just walk over to the bad guy and swing away whenever they try to escape.
I think you need to find a way to make a new class more unique. I also hope I didn't come across too harsh. Just trying to get you to think about a role that needs to be covered in game that you can do in a unique way. A lot of what you've presented is more of a mash up of already existing class features from classes that do the job really effectively.