For example:
example.com
and example.net
).Overall, your setup looks fine. Hope you've covered handling session expiry/timeouts.
The only issue (and its more of an inconvenience) I see is the need to click 'Log in' explicitly. Personally, I prefer auto logins (like Google, MS and ton of other major sites).
SO detects if you've a valid login and shows a message asking to refresh the page. While somewhat annoying, it still at least tells me that I'm logged in.