Since both your sister and father can sign on with their ID's and you can't, then the problem is surely your ID. You need to call Apple with the Code and explain the problem with your ID so that they can remove the block. Good luck.
I printed the 3 customer Codes of each of my 3 Apple ID`s,called Apple Support from a cheap Internation calls (call center) after i finnished work.
I got lucky enough to be on contact with a good guy,i told him that i have problems signing in to iMessage and FaceTime with my Apple ID`s on my MacbookPro but my father and two sisters were able to sign in with their Apple ID`s without a problem.
After i gaved him my first apple ID and customer code,he just asked security questions to verify that its me,he said ok i got you registered now and you should be able to sign in without a problem man.go enjoy chatting on your macbook.
i Told him that i have Pages,Numbers,Keynote,iMovie on one of my apple id`s when i caught them while they were free,so i dont want to spend extra around 100$ again,can u fix the two other apple ID`s aswell so i can check which one had it,and use that as my main account after.he registered the two others aswell. All fine.
But after i came home,i tried signing in,none of them worked,same error codes again,i guess ill`have to wait 24-48hrs and try that again since many people reported here and on p1lgrim`s post that it didn`t work right after but after like 24-48hrs they were able to sign in without a problem and use iMessage and facetime.i just hope its the same case with me aswell.