Seriously, I think the adoption system in Hearthfire was actually cut content from the vanilla game (possibly due to the 11-11-11 deadline). Consider much of Honorhall's dialogue.
Constance: "I'm sorry, the children aren't up for adoption right now. You should leave." (implies that they might be up for adoption later, after Grelod's "departure")
Runa: "...Come on, adopt me. Pleeease?" (why would she say this if it weren't possible)
Hroar: "It's too bad the orphanage ain't lettin' us kids be adopted. I'd be the best son ever." (similar principle)
Grelod: "I'll hear no talk of adoption!" (yes, she's not allowing it, but she's not long for this world)
Also, you're allowed to get married and own homes, and parenthood is a natural extension to this. And note that all five of the "vanilla" homes could be outfitted with a kids' bedroom, some of them without deleting any existing stuff.