changing country causes problems with my iCloud and login

I spend 6 months each in Sweden and California, have an iMac in both places (2011, OS 10.11.4 and 2015 El Capitan). Each year, when I return to Sweden I have problems with the older Swedish iMac not recognising me, and I get strange questions like ˜The System was unable to unlock key chain˜, ˜Message agent wants to use the login key chain˜. Also, an email address I have used for a long time is not recognized, so I can not log into FaceBook. I had to give up my very old Swedish Apple ID and loose all music purchased under that ID. Each year I have to contact Swedish Apple to get help. The Macbook Air I carry with me helps me while I struggle with the Swedish iMac. Anyone else out there having similar problems?