Dr Pepper/7Up company is its own thing. RC Cola is the cola they make.
I guess Pepsi used to own 7Up but still own the rights, and that would explain why you can get 7Up at places that serve Pepsi but not Dr. Pepper.
Huh, that must be a regional thing. Places I go to that serve Pepsi products always have Dr. Pepper, but never 7Up.
Dr Pepper is almost always distributed with Pepsi, and is often distributed with Coke. It's distributed less with Coke because Coke own Mr. Pibb, but you still see it often with Coke because it's way more popular than Pibb, and because it can still be freely distributed since it is independent of either Coke or Pepsi. So if a restaurant wants Dr Pepper instead of Pibb, they can usually get it, although it depends on distributor availability in the region.
It's kind of the same thing with 7-Up and Sprite. Coke owns Sprite, and 7-Up is independent (part of the same company as Dr Pepper actually). That's why you almost always see Coke and Sprite sold together and Pepsi and 7-Up sold together. Though technically it can go either way. However, it is rare to see Coke sold with anything other than Sprite, because Sprite is very popular and doesn't turn off customers the way having Pibb instead of Dr Pepper does. Pepsi actually owns Sierra Mist though, and do to the declining popularity of 7-up, I wouldn't be surprised if more and more places are stocking Sierra Mist with Pepsi instead of 7-up.
They renamed Sierra Mist to Mist Twst (no, that's not a typo, that is how they are spelling it).
But now they also have Mtn Dew Ice, which is a caffeinated lemon lime soda. Kinda surprised there isn't Diet Dew Ice yet. ---