how do unlock a locked AppleID on iPhone plus?/

I use an iPhone 6 plus, same with my wife

We found out our ID profiles have been mixed up i.e my pictures syncing to her fone and vis-vasal. My Apple ID shows my correct ID but my wifes' name on the iCloud on my phone. I have tried signing out iCloud but each time it will ask to sign in with my Apple ID to turn of the find my phone feature. I have reset my ID password and have successfully used it to sign in to the App store but still cant use it on my phones iCloud.

Help anyone!!