OK this all makes a bit more sense now, as @apcyberax says the move and transfer operation is only applicable when you need to move all of the email accounts (both primary and secondary) to a new VM account and officially the two account holders need to be the same person. So I don't think this is going to fly in your case unfortunately.
Is you Dad still a VM broadband subscriber (please say yes!) If so then if he gets in touch, possibly on this forum, and tries to get his main account password changed - I assume he (or you on his behalf) has already tried the forgotten password options and answer the security questions, then armed with that he can then reset the password on your secondary account and also your sister's as well. If everyone is in agreement then you could just carry on like that, but, of course, your email address still won't be yours, your Dad would be in control of it.
Unfortunately because your Dad is the account holder, VM will only deal with him on this matter.
Personally, I'd go down this route, gain control of the mailbox, copy out anything you wish to keep then set up a new Outlook or GMail etc. account for yourself, you can setup automatic forwarding from the old virgin.net mailbox to your new one and at some point ask your Dad to delete it.
Bit of a convoluted path, I agree but I can't see any other way of doing this.
Good luck!
John