A quick puzzle

Bart was going to throw a party. His space was limited, so he couldn't invite all of his friends. After much thought, he came up with his guest list. He invited his friend Stewart, but not his other friend Stuart. He invited Edward, but not Eddie. He included Dave & Drew, but not David or Andrew. Fred got an invite, but Frederick didn't. The party had to include Steve, but Steven didn't make the list. He needed some girls, so he asked Rebecca and Barbara to come, but he didn't ask Becky or Barbie to join them.
With this in mind, who should chaperone the party, Mom or Dad?