Interesting indeed. While I'm looking into how Tracert name resolution is performed, it does look like you're still having DNS issues. It would appear that your workstation uses 192.168.4.254 (my.router) as your DNS server. I would verify the DNS forwarders on this device - which typically point to your ISP's DNS servers.
I would make sure you can ping the IP addresses for these DNS servers. You can also use the following commands to test the remote DNS servers for name resolution:
nslookup
server x.x.x.x (where x.x.x.x is the IP address of your ISP DNS server)
www.diplomat.co.uk