Okay, I don't know what I'm doing wrong. All I'm trying to do is get Lydia and Lucia into my house in Falkreath, Lakeview Manor.

In Lakeview Manor I have a child's bed and a child's chest built, but everytime I talked to Lucia and told her I could adopt her, the only dialogue choice I got was "I have a house, but no room for you." I finally replaced my alchemy lab with her room in Breezehome, but now the option to move is gone whenever I talk to Lydia.

Is this just a glitch or am I stuck with a useless bedroom at Lakeview and Breezehome my real "home" now since my wife and daughter are stuck there?

I think you need 2 child beds and the players bed before you can move the family in hearthfire houses.

Moving the family from Breezehome is a much discussed bug. Try completely furnishing Lakeview for two children and the wife then give it another shot. if it still doesn't work you may be out of options.