The bedrooms.

What I want to know is, would the steward and housecarl sleep there as I'm planning, or would building that wing cause my character's wife and kids to relocate although they already have their own beds?

I believe that once you build the bedrooms, it becomes your family's sleeping place, though you can sleep in any bed not tagged "Owned."

Stewards/Housecarls sleep in any other free beds but the bedroom ones.

I remember I had Steward-Lydia sleep in what was once the main bedroom on the second floor, but Steward-Roggi slept on the crappy beds on the other side. Husband-Roggi relocated to the Bedroom once he was married, though, so yeah.

Sounds like I got everything backwards then.