Hello.
As long as you do not have links such as
http://www.yourdomain1.com/index.php on your
website hosting, and insteas just /index.php, then the second parked domain will not be redirected and will appear independant.
I'm sure eUKhost will still register your free domain for you, but you'll need to contact them about this issue - support [[at]] eukhost.com
Good Luck!