The direct object of the sentence is "her."
In the sentence "Kimi asked her mother to come and pick her up," the direct object is what is being asked for or referenced, which in this case is who Kimi is asking (her mother). However, the phrasing "her" at the end refers to Kimi.
To clarify, the direct object of "asked" is "her," as in "Kimi asked her."
If you meant to refer to the person mentioned as the recipient of the action, "mother" would be the object of the verb "asked" (who Kimi is asking), but the direct object regarding the action of "asked" specifically pointing to Kimi herself would be "her."
So, it is best if we clarify that "mother" is the noun that Kimi is asking, while "her" indicates Kimi herself in the structure of the sentence. Please specify if there's confusion about the terms!