Member of the Pontiac Tribe
There was a Pontiac Chief and also a Chieftain
Line of Dodges
Dodge models included the Stratus (which means 'layer') and the Caravan (which means a convoy of travellers).
Supreme Chrysler
the Chrysler Imperial, perhaps? Or perhaps the Executive?
Pierce sticker
Their emblem was an arrow
Jeep Horse Whisperer
A horse whisperer (and also a model of Jeep) is a Wrangler
Trusty Isuzu
Both the Isuzu Trooper and Amigo lines would fit this clue
Edsel woe
I thought the entire range were regarded as a failure? In this context, the Citation seems the most probable answer, since it would be a 'woe' in the traffic sense.
Fearless Dodge
Intrepid, surely!
Words that fit with the theme:
Trooper, Chief/Chieftain, Citation, Intrepid, arrow, Wrangler
Words that don't fit:
Imperial/Executive, Caravan
As I see it, there's multiple ways that the blanks can be filled, while still making a legible sentence. One possible solution is:
The Trooper wrote the Chieftain a Citation causing him to visit the Intrepid warrior, who shot an arrow through the traffic ______ heart.
I still think that
Wrangler
ought to fit in there somewhere.