How does the Sentinel feat interact with the Mounted Combatant feat?

When a character with the sentinel feat hits with an opportunity attack against an opponent with mounted combatant, does the mounted person need to stop moving?

Sentinel feat gives the below ability, which is usually clear in its applicability

When you hit a creature with an opportunity attack, the creature’s speed becomes 0 for the rest of the turn. (PHB chapter 6 – page 169)

It seems a bit ambiguous regarding controlled mounts, due to the way movement rules work, and the way mounted combatant redirects attacks.

The relevant text of mounted combatant, from PHB:

You can force an attack targeted at your mount to target you instead. (PHB Chapter 6 – page 168)

And on controlling a mount

The initiative of a controlled mount changes to match yours when you mount it. It moves as you direct it, and it has only three action options: Dash, Disengage, and Dodge. (PHB Chapter 9 – page 198)

So suppose the scenario is as follows; Person A has sentinel, and on Person B has mounted combatant, and is on a mount. On their initiative th mount goes, and they get within reach of A, and get hit with sentinel’s opportunity attack as they try to leave. However they redirect the attack from their mount to themselves.

While the sentinel person’s attack was aimed at the horse, it ends up hitting the rider. However the rider isn’t actually using their own movement here, the horse is. Does the horse/rider pair stop regardless as they are moving together? Is there some weird interaction where the rider is stopped, the horse is not, and they perhaps have to make some sort of save to stay in the saddle? Or does mounted combatant negate this portion of the sentinel feat, rendering it ineffective?