The children´s beds are supposed to be "owned", or at least that´s how it´s been for me always.
Have you built up everything? At least the bedroom addition completely, and perhaps the main hall (including upstairs, downstairs, and the little room behind the fireplace)? Those _may_ sometimes cause the problem - I also may be totally mistaken here, sorry, just trying to help :)
At least the "owned bed" -thingy should not be the problem here :p
Ok. I just tried it, went to adopt kids, checked before leaving that yes, beds are owned even when there are no kids in the house yet. I tried to adopt and was totally able to do so (fully furnished Lakeview). Also noticed: the kid´s beds in each home I have are indeed owned.
Hmm.. it is said though, that sometimes it lets you adopt even if you haven´t met the requirements yet (meaning the chests etc) and vice versa, Idk.. hope you´ll find a solution :(
Same thing happened to me. I had a mod installed so I could have 6 children’s beds, I had breezehome, and it said every bed was owned.