One of the daughters recorded the heartbreaking scene on her cell phone.
Her father, 48-year-old Romulo Avelica-Gonzalez, is undocumented and has been in the United States for 20 years.
Garcetti says the arrest is very troubling and says we need more details.
"We want more answers," Garcetti said. "And we need to make sure that this is not the beginning of a dangerous and dark time here, where people are afraid to go to school, people are afraid to drop their kids off, people afraid to go to work. That would be troubling for our economy and the safety of our streets."
The father has been granted a temporary stay, and has been moved to a detention center in Adelanto.
An attorney who is fighting to keep him in the United States believes he was detained in part, because of a DUI conviction nearly a decade ago.