Welcome to the forum @Ozgur
Happy to offer a bit of advice, but I need a little more information.
For clarification, there's secondary Optusnet email address attached to your parents’ Home phone and broadband account?
You're wanting to transfer that email address to a mobile service, do I have that right? Let me know.
So basically when Optus sport was first introduced I signed in with my email under my parents internet subscription and now that I've got my own Optus Sport subscription with my plan I cant change which account my email is linked with.