Login to Google Analytics
I'm no Analytics Guru, but logging the user in automatically might very well be impossible due to security restrictions.
Logging in on server side, and proxying the data to the client, is a bad approach even if you get it working, because there's a lot of Ajax involved and stuff can break any time.
Possible alternatives that come to my mind:
Adding guest accounts to the analytics account that are allowed to view the stats but not change anything (The user would still have to authenticate)
Fetching data using the API (Obviously much more complex than what you have in mind, but as far as I can see the only method that can work completely automatically)
Recommending the user to activate browser-side password storage - with all the downsides this includes