Now, if your question was about fixing the issues rather than other providers, my answer would be this:
For the loading times, are you using the new interface or the older one? There is a list at the bottom. You could try older version or basic HTML.
Settings > Chat there is a setting that acts as chat permissions:
If you aren't already, try the 2nd setting. Though as you can see, the first option still shouldn't have random people messaging you. I've never had this issue and you can see my setting.
As for the infinite redirect loop, you could deleting the GMail cookie. Are either of you checking the box to remember you when you sign in?
This question would also be useful: http://webapps.stackexchange.com/questions/3423/how-to-manage-multiple-gmail-accounts-on-the-same-pc-browser