Both Molly and Amy (in the OT) have gotten confused and assumed that the accounts had been merged indefinitely (who can blame them? This is as much PEBKAC as horrible UI) so they attempted to "unmerge" them, ending up deleting one of the accounts.
The way to "unmerge" them is to log out of Google. Then, next time somebody logs in, there will only be one account.
This UI is horrible, I had a similar uncomfortable moment trying to log one account but not the other, even though I knew that they had not gotten merged, it sure seemed like it. The intention was good, the execution lacking (my guess is that there were lots of technical reasons this couldn't be done cleaner).
As soon as Chrome introduced Multiple Users[2], I started using that and it's much better, with less mental overhead to check which account is loged in (I use a black theme for one account, a white theme for the other). For other people/accounts, I just use Incognito mode. For most end users, this is still too much overhead for them, but in that case the only solution I could see is autologout, which has its own problems.