So Rigger 5 mentions several times that Ares is releasing vehicles under the Dodge brand, but I can't find anything anywhere else about Ares owning Dodge, or Sony allowing Chrysler-Nissan to sell Dodge to the owner of GM-Honda? Is it buried somewhere inane like Court of Shadows?

Probably the usual where the writer didn't do their background research.

I believe Ares owning Ford dates back to SR3, but I don't remember Dodge. Perhaps it was a recent acquisition?

Ford was an independent corporation in SR3 Rigger 3 (page 19) and Corporate Download (page 40). Ares Macrotechnology had (re)acquired General Motors in 2059 to establish its automotive branch (including the Buick, Cadillac and Pontiac brand). Dodge was mentioned as a Chysler-Nissan corporation brand in Shadows of Asia (page 10).

Ah, must have been General Motors I was remembering. I wonder why Ares hasn't just bought them all and re-purposed them into "Ares Autos" as their flagship car manufacturer.