The story gives some clues to understand why Diaz thinks about Yunior's motion sickness. Firstly, the father warns the mother not to feed him before the car travels. Thus, when Yunior is full driving, it is relatively higher possibility that he will vomit. Thus, his stomach is sensitive to the motion, and if his stomach is empty, he can stay without vomiting in the traveling car.
Also, in the car, Yunior tries to stay still. There might be two reasons behind this: 1) he does not want to attract his father's attention on him and 2) he wants to stabilize his stomach not to suffer from the motion sickness. Thus, if he concentrates on different things inside the car, it disturbs his stomach, and he suffers from the motion sickness.
Another clue is that the father cleans the car one day, and he finds out something smelling inside the car. He assumes that this smell is disturbing his son's stomach during the car travels. However, there is not certain information given in the short story what happened after the father has cleaned the car and informed the family about the smell.
Consequently, there is no certain information why he has the motion sickness. However, it sounds like somehow psychological, and some simple solutions his family suggests him works to overcome this problem. For instance, his mother gives him a menthol candy, and it helps him to keep his stomach away from the motion sickness. Also, when he concentrates on the road, he does not get disturbed from the motion sickness.
Some people's stomach might be very sensitive to the motion. Especially, traveling might be difficult for these people because the moving car shakes their stomach, and they throw up. The motion sickness might be psychological or the result of real sickness.
How is that problem connected to the rest of the plot?
The story sounds like a story on a Latin American family immigrated to the US. The family struggles for developing their lives in the US. Because of that, the family members carry some stress on them. The family is also a traditional male-dominant family. The father makes the decisions for the family. The father works outside the house while the mother stays home and grows her kids and take care of the house works. The kids have some responsibilities, and they are not free individuals. The father and the mother make decisions for them, and they hesitate to speak against their parents.
Yunior sounds like the youngest member of the family. He finds the life stressful, and he does not feel comfortable inside the family. All the other members request him to do something while he even cannot speak against them. Because of that, he would like to go out freely and not to answer the questions his parents ask him.
He has the motion sickness, and this sickness influences him deeply. He defines others' reaction to him around this sickness. Probably, his father mentioned his sickness as an important problem because he throws up in the car, and he has to clean it or get the car cleaned. In another word, this sickness determines his relations with the other family members. Simply, this sickness makes him disadvantageous in the family.
During the whole story, he remembers some past happenings around his sickness. For instance, his father has a relation with another woman, and he met this woman thanks to the car travel with his father. The only time his father took him out for a car trip is thanks to his sickness. Also, his father seems to be angry with him because of his sickness or he feels like that.
He defines his relations with the other family members through this sickness. His mother is very caring on him, and she always tries to make him relatively better by giving him some candies and help him feel relatively better. Consequently, he sounds like a bored family member and he observes his family members' reactions to him through his sickness. His sickness looks like one of the most influential things on his ideas and his life. He does not even bother developing a new thing in his life. In fact, he is a little child and he receives the reactions from his family members without giving them a reaction back, he accepts them.