The worst part about chrome for me is that I can't access my Gmail accounts through Chrome. That's right, I have to use Firefox to access Google's own product because Chrome won't play nice with my school Google Apps account that my school provided us for email. Whenever I try to get to my school account it redirects to the gmail account I used to sign into Chrome - this happens regardless of whether I try to access the account directly through the school's website, or through the gmail website. The only way to get around it is to completely sign out of the browser, restart it, then make sure I don't visit any other sites than my school email. Obviously this is an enormous hassle and it wasn't always this way. I used to be able to use the multiple accounts feature with ease until one day Google up and broke it.
I share your pain. One way to get around it is to use the Chrome 'multiple profiles' feature, it lets you switch to a different 'profile' with entirely different cookies, cache, etc., and will let you sign into a different Google account than in your first profile.
You can switch profiles and even have different profiles active in different Chrome windows, without restarting Chrome.
(I am not saying this makes it all better, trying to use more than one Google account is a _mess_ no matter what. But that it's one workaround I discovered recently, which has been lessening the pain somewhat)
The profile switcher is nice - would like Firefox to support fast switching out of the box. But here Chrome is going a little backwards too. Recent work has made that profile switcher a bit less convenient. Many complaints here:
https://code.google.com/p/chromium/issues/detail?id=403619
This does happen to me sometimes. I'm a consultant so I end up having to use customer gmail accounts and my personal account. So of course it always logs in with my personal since the browser logs in with that. Then I add this customer. Sometimes when I click to switch accounts it keeps sending me back to my personal account. I'm sure someone from the GMAIL team is on HN so they might see this.
That list is totally broken, it won't update when you get logged out of one of your accounts, and like you've seen if you try to go to one of those accounts, you get bumped over to the one you're still connected to. If you do the "add account" thing and add the one that's not working, you'll be authenticated and able to switch back and forth for a while.
The same problems exist in Firefox, too - I open a private browsing tab when I need to access my work Google Apps account when I'm logged into my personal Gmail account. Google's multiple-account login system is just totally broken, it would be less frustrating if they didn't offer it at all.
To me that sounds like your school's sysadmin team is to blame, they don't seem to have figured out SSO. Both schools I've gone to (undergrad and graduate) had perfect Gapps integration, and both work perfectly in Chrome.
They have some other issues as well, the wireless is very difficult to connect to and the "program" that we had to download usually does not work. Android devices were not even supported at all until sometime in late 2013. The print queue is constantly frozen, and a few other problems I can't think of off the top of my head right now. All of this is strange because from what I understand the school has a decent computer science program but I was in humanities so I'm not sure.
