What's the trick to the cart race?

If you smash into your enemy's cart, you have slightly less than a second before the horses start going left again. The object isn't to destroy your enemy's cart, but to survive the road ahead. I finished it without destroying the enemy cart.

All you need to do is hit your enemy's cart right before you cross some rubble. You'll dodge the rubble, and then the horses pull left on open road instead of the broken bits of road.

Theres a part of luck in that Sequence, I'll give you that.

The trick is to time the places where you'll kinda stick with the other cart to dodge the rubble.

I didn't really like that part for that lack of strategy in use.

You don't destroy the enemy's cart; you simply survive.

Leandros will try and ram you if you get too close. Keep your distance and don't go in the offensive. Steer clear of the rocky patches and you should be fine. When you reach a certain point, a cutscene will trigger. Leandros will yell to his guards, one of which will throw a grenade under your carriage, causing the carriage and Ezio to go flying over the canyon. As a result, Ezio is severely injured, and the mission "The Wounded Eagle" will begin. So you're not meant to destroy Leandros' carriage. I do not even know if it's possible.