Motivation cannot be revealed through a dialogue.
(a) A character can give a narrative of a part or parts of the story (exposition) to another character. For example: Jane says, "Yesterday, it was raining hard. I can see my mother, who was from work, soaked and coughing."
(b) A character can have a dialogue about conflict, too. For example: Jane says, "I don't know what to do. Do I stop going to school and work instead? Do I leave my mother to suffer from her sickness?"
(c) Motivation is NOT a narrative element. It can, therefore, be eliminated based on this ground alone.
(d) Though not common, stage directions can sometimes be used in a dialogue. This is common in modern plays. For example: Jane says, "I move forward, and reach out to the audience. Can you see my tears? Can you feel my pain?"