大人 and 子供: adults, children, and one's offspring
Separate age categories from the relationship of being someone's child.
The adult category
大人 (おとな) means adult. 「大人二人で予約しました」 says the reservation was made for two adults.
Check the relevant notice for an adult fare's age threshold. The word 大人 alone does not set one uniform threshold for every service.
Children and offspring
子供 (こども) can mean a child or someone's offspring. 「子供が公園で遊んでいます」 describes children playing in a park.
「私の子供はもう働いています」 can refer to offspring who already work. In a parental relationship, the person need not be a young child.
Identifying the classification
「大人も子供も参加できます」 permits participation by both adults and children. This context separates age groups.
「子供のころ、この町に住んでいました」 means living in this town during childhood. Whether the speaker still lives there is separate information.
Must 子供 in 「私の子供はもう働いています」 refer to a minor?
Show the answer and why
No. It describes the parental relationship, so the offspring may be an adult.