The direct object of the given sentence is "her." In the context of the sentence "ask her mother to come and pick her up," "her" is what the mother is being asked to pick up. If we break it down:
- "ask" is the verb.
- "her mother" is the indirect object (the one being asked).
- "her" is the direct object (the one being picked up).
So, in this case, the direct object is "her."