Additionally Ignoring the illegality of prosecuting asylum seekers and setting aside the fact that there is no requirement to prosecute, illegal entry is a misdemeanor offense. Illegal entry is most similar to technical violations of motor vehicle law, such as driving without a license, not breaking and entering, because it amounts to nothing more than movement without a proper permit. Many misdemeanors do not even require police to take a person into custody at all. A variety of traffic offenses—including driving without a license, operating an unregistered vehicle, speeding, and other offenses—are misdemeanors in dozens of states. In general, police simply issue a summons to appear in court (for an example, see the Virginia code here). If a child is in the vehicle, they are not separated from the parent pending the final dispensation of the case.
In the unusual cases in which a parent is brought into custody for such a violation, the children either wait in the police station while the parent is processed or are handed off to a relative. For example, in the case of Gail Atwater v. City of Lago Vista, a local police officer arrested Atwater for a seatbelt violation with children in the car. The officer initially said that the children could come to the police station, but allowed a friend of Atwater to pick them up. In other words, there is a massive difference between the treatment of minor offenses committed by Americans and these parents coming to the border. Moreover, if U.S. parents and children are separated for these types of offenses—as in the Atwater case—it is an outrage, not a justification for further separations.