They would only receive Advantage on AOO if they use one of the 2 aforementioned ways to 'brace' (Ready Action, or Polearm Master).

Otherwise, they have normal AOO and non-polearms have Disadvantaged AOO (if they are hit by the mounted combatant).

I guess ultimately this is more of a polearm/mounted combat interaction homebrew.

I guess the Disengage action makes sense as well. I searched and Mike Mearls would interpret it as the rider not provoking AOO if the mount disengages, which seems like a nice idea.

Also, I disagree about mounts being strong. Most will die in 1-2 hits, and they can be quite expensive (400gp for a 11ac, 19hp warhorse).