Time Machine is dedicated to one computer. Do you mean that the drive is shared, and you want to copy a clone onto that?
If your parents live nearby, you're better off transferring the backup the old-fashoned way (by going there in person). Cloned backups are huge, and even on a decent connection can take weeks to transfer.
I know some people around here use two Time Machine drives, keeping one at work and one at home. Every week, they trade drives, so the work backup is never more than a week old. I think that's the ideal solution, since maintaining a dedicated off-site backup can be a lot of work and it's easy to give up altogether.
Security isn't an issue in any of the methods I mentioned, assuming that the drive is stored somewhere safe. If you do want to transfer files remotely, the security depends on what protocol you use. FTP isn't secure, but SFTP and AFP are. Regardless, if you're making a SuperDuper backup, I suggest backing up to an encrypted DMG.
