The incident happened near at Bullard and Helm on Tuesday afternoon. Tuesday was the second day of the district's new fall semester.
Police say the woman drove away after side-swiping the other vehicle, but pulled over a few blocks away. No one was injured.
The woman had a BAC level of over four times the legal limit, according to police.
She is facing charges of felony child endangerment and DUI.
Police say the suspect's child is with a trusted relative.