I'm back from work and tried this again. This time I deleted the passwords instead of cookies and I got the same strange results. Sometimes it logs in correctly, sometimes not (goes to account #1).

But I did find a workaround. I logged into my main account and choosed "Add another account". When logging in into my main account and choosing my other account inside of it I go to the other one without any problems. Since this takes about as much time as to logging out one account and logging into the other it's a very practical workaround indeed