Object direct or object prepositional

[Melisa85]

The grey mare (S) rode across (V) the field (Object D) with great care (Adv).

The grey mare (S) rode (V) across the field (Object prep) with great care (Adv).

Is the rode across (predicate) and the field (object direct) or should rode be alone as a predicate and across the field (object prepositional) ???

I'm confused when the preposition goes with the verb and when with the object. If a verb is a phrasal does it always have to be followed by an object direct????

[bhaisahab]

Strictly speaking a horse doesn't ride, a rider rides a horse, a horse walks, trots, canters or gallops.

[Melisa85]

But if it was another verb like walk where would across go??? With a verb or with an object??

[bhaisahab]

The grey mare (S) walked across (V) the field (Object D) with great care (Adv).