If you take a dog as a sidekick, do you lose your humanoid sidekick?

Nope... you can have both.

If only you could combine them

Ugh, the dogs never, ever, shut up though. I found the barking so annoying. It apparently doesn't effect anything. Well, except my mental well being. It does make my dog watch the TV while I play though which is pretty comical.

I actually wanted the dog to stay at my house but that doesn't work out. Maybe I'll use the dog as a companion when I play as a hunter that avoids the cities.

You can have both. And I'm loving my dog right now. The barking was damn annoying so I got a mod to tone that down. Also wasn't a fan of the vanilla dogs look so he's a white wolf now. Kinda makes me feel like one of the Stark children with their direwolfs if you've ever read ASoIaF.

The very few times I've had a dog follower, the little bastard kept nudging me forward as I tried to remain hidden. Bad dog.