Learn Russian: Сестра любит катать младшего брата в коляске. - The sister likes to give her younger brother a ride in the stroller.

катать is the multidirectional verb of motion. It is used here for two reasons: first, the sister likes doing this in general (a habitual action after любит), and second, pushing a stroller around usually involves moving in various directions rather than making a single, one-way trip from point A to point B (катить).

Could we use the reflexive verb кататься in this sentence?

No, because the sister is performing the action on someone else. катать is a transitive verb, meaning it takes a direct object (младшего брата). If you used кататься, it would mean the sister is riding in the stroller herself.

Why does the direct object младшего брата look like it is in the Genitive case?

Because брат is an animate masculine noun. For animate masculine nouns and their matching adjectives, the Accusative case (which is required for direct objects) takes the exact same form as the Genitive case.

Why do we say в коляске instead of на коляске when talking about a stroller?

A baby stroller (коляска) is treated as an enclosed space, so the child sits inside it, requiring the preposition в. For things you ride on top of, like a bicycle or a horse, you would use на.