Answer:
The mother - subject
The children - indirect object
The inflated beach ball - direct object
Step-by-step explanation:
You haven't pointed out which word is underlined, so I wrote what the functions of all words in the given sentence are.
The subject is what the sentence is about. It's what/who performs an action expressed by the verb (here - gave) or is being described. In this case, it's the mother.
The direct object is the recipient of the action expressed by the verb. Here, it's the inflated beach ball.
The indirect object is the recipient of the direct object. Here, it's the children.