Shielded Stride while Mounted

Pathfinder 2E

I’m building a Human Fighter into a sort of Knight character. I was curious about the 4th-level Class Feat Shielded Stride. The feat reads

When your shield is up, your enemies’ blows can’t touch you. When you have your shield raised, you can Stride to move half your Speed without triggering reactions that are triggered by your movement (such as Attacks of Opportunity). You can use Shielded Stride while Flying or Swimming instead of Striding if you have the corresponding movement type.

This feat is a feature and not a feat that requires an action in order to use it. So my question is, if I

  • Mount a horse (1 action)
  • Raise Shield (2nd action),
  • Command Animal (3rd action, my part)
    • Move/Stride (3rd action, horses part) (only moving half of it’s speed as the feat requires)

Would the horse’s movement trigger any reactions, such as Attacks of Opportunity or would it not because I have taken the Shielded Stride feat?

A similar, but opposing question: can a horse’s movement be used within Combat Feats like Sudden Charge? I would hope so, but if my understanding is correct the horse’s movement has the prerequisite of me using Command Animal to make it move, while Sudden Charge’s movement is included within it’s 2 actions.