"Barrel racer" and "laid back" should ALWAYS go together. A proper barrel horse should be smart enough to know when to switch on and off.
I'm not really knowledgeable about bloodlines, although I hear the Dash for Cash and Easy Jet lines are supposed to be good for barrels, and the name Firewater Flit comes to mind first when I think of barrel horses...
My sister's mare is a Doc Bar mare (sired by Lena's Playboy), and she's a pretty good mare. From what I see, they seem to be more cowey, but the mind is there. She is definitely athletic and if she had had a proper rider, could have done very well. She's a bit too sensitive for me, but overall calm and a sweet, sweet mare.
I ran barrels on a quarab, if you'd be interested in that. He didn't have any notable breeding, but he was a good little horse. He had plenty of speed, and a pretty good turn on him. Of course, since it's a breed cross you'll have to be pretty picky, but you can't be unhappy with a good quarab :P