Answer:
The mother - subject
The children - indirect object
The inflated beach ball - direct object
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 - <em>gave</em>) or is being described. In this case, it's <em>the mother.</em>
The direct object is the recipient of the action expressed by the verb. Here, it's <em>the inflated beach ball.</em>
The indirect object is the recipient of the direct object. Here, it's <em>the children</em>.