Don't get operating subsidiaries and codeshare mixed up, these are two different things entirely. Flights to Cody and other smaller airports that are under discussion here use UA codes and are treated completely as UA for revenue purposes, thus reward seats may be available, even though they are operated by a subsidiary/contractor (i.e. "Skywest d/b/a United Express"). This is the same thing as in Australia where
Virgin Australia Regional Airlines (VARA) and various Qantas subsidiaries operate flights under their respective parent airline's code. The operating contractor is more of a backroom detail that doesn't directly impact your experience - you still deal with United for check-in/customer service, the staff usually wear United uniforms - for all intents and purposes it's a United flight. (The famous "doctor-dragging" incident involved an operating contractor but United themselves took full responsibility as their brand was on the plane.)
Codeshares are a different arrangement where a totally independent airline operates flights under its own metal, and another airline like United adds its code ("markets" the flight), for example flights from DEN to FRA on Lufthansa may have a United codeshare attached. These flights are not available to
Virgin Australia reward members as they are Lufthansa flights. The flight in this case is operated entirely by Lufthansa, you check-in with Lufthansa, everything is Lufthansa service levels and uniforms/livery, it's just that you bought your ticket through United's web site as a sales agent. (You can buy United revenue flights this way through
Virgin Australia.)
BTW, depending on where you are going in Yellowstone, consider Jackson Hole (JAC) as an alternate. It has direct flights to LAX at certain times of year, convenient to Australians connecting from SYD/MEL. There's also IDA (Idaho Falls) with scheduled commercial service, though this would be similar to Cody with service only to/from Denver.