I haven't been able to adopt. I have a home in whiterun, solitude, and now falkraith. I went to try to adopt Sofie from windhelm and it won't give me the option to adopt. I do have two other children but they are at different houses. How to I do this?
You may only adopt up to two children in an un-modded Skyrim game. You say you have already adopted two children, so you won't be able to adopt any more even if the ones you have are living at different properties as you're at the adoption cap.
There is a Multiple Adoptions mod available that raises the limit to 6, but it recommends starting a whole new game due to the way already-running scripts are written into the save data.
You can adopt up to 2 children, unless modded. There are 5 places where you can adopt children. You will also need to completely furnish you homestead if you want the family there. Otherwise, if you live in a city house, buy a kids room.
Dawnstar Quickysilve Mines: Alesan
Solitude Katla's Farm: Blaise
Whiterun Gildergreen: Lucia
Windhelm Dock Gate: Sophie
Riften Orphanage [Must complete Innocence lost, which starts with Aventus Arentino in Windhelm]: Runa Fair Shield, Samuel, Francois Bueatfort, Hroar.
If you want to adopt more than one children, get the Multiple Adotion Mod so you can adopt more than 2 children in the game.
For unadoption, get the Unadopt Children mod which adds a power to reset childrens' al.
You will see orphans in some towns. If you go to them and speak with them you'll get a option to adopt them in the further dialogues.
Mostly there is some kind of dialogue option like this: I could adopt you, if you want.
You can find a list of adoptable children here.