Can you give an example of a series of actions that leads to this? I'm logged into two separate Google accounts at pretty much all times, and I never run into trouble. I'm curious as to what the difference is between our two usage patterns.
Scenario 1) I have both open, and log out of my gmail account. It redirects to my school's "goodbye" page. I just reproduced this. Not a huge problem, but indicative of a bigger issue.
Scenario 2) Now log out of the school account. I am greeted with a login for my gmail account. This is pretty close to the problem in Scenario 3, below.
Scenario 3) The real issue. The problem is not so much that it has happened, it's that there is no way to recover if you don't have the password. The other week I logged into my wife's laptop to grab a document from gmail to print, since it was hooked up to the printer. She didn't use it for the next few days. When she went to her work email's address (a .gov domain), it prompted her for my gmail password. There was no way to 'change account' at that point. No way to log out. Go to the .gov domain, get a prompt to login as <me>@gmail.com. No way to authenticate. I couldn't figure it out, and finally just logged in as myself then logged out, after which I was redirected to the .gov boodbye page, but it allowed her to log in after that.
Edit: Scenario 4) Go to www.gmail.com/a/umbc.edu, which the google help pages say is the correct way to go to the school's site. I just tried this, and it sent me to my gmail.com inbox. It is pretty much a crap shoot which mailbox I get when I first load the page. Sometimes it's aware I'm signed in under different IDs, sometimes not, so I can't always change accounts, and must go through login/logout hell to get them clear. Perhaps I could just clear my cookies but I don't like doing this en masse.
Whichever one says /u/0 is the first one you logged in as, and that will be the default if you, say, open a new tab and paste in a bare link (without /u/ in it).
If you want that to be your personal account, you can make that your /u/0 account by doing this:
1. Log out of all your Google accounts
2. Log into your personal account
3. Click the picture in the upper-right
4. Click "add account"
5. Log into your work account
Regarding your second: Citation needed. There's this persistent rumor that if you make a G+ account with a fake-sounding name, Google will lock you out of your GMail and erase all your Google Docs, but as far as I've seen, those rumors have never checked out.
...until two or three days ago.
GMail flat-out refused to let me log into two accounts (it would end up in endless redirect when I tried the second one - I quit Chrome, fully cleared cookies, history, everything... it just would not work)
It seemed to have cleared up by the following day.
These types of things are what I think about when people tell me how great the Google programmers are, but that's another topic.