Well there are a few things that do not add up: You are presuming Android is refusing to connect. I can understand the first "Connected but no access to the internet" that is a config issue.
But the second is a router not allowing access, a different config issue; I doubt it is Android.
Then: all three have connectivity issues?
May I ask why you chose to use domains and not just basic settings?
edit
You may be having IPv6 issues: