Tap and hold on the account you want to delete. A drop down menu will appear and then you can choose the delete option.
If you had the first account setup and using the Xbox Live function I'm not sure if deleting the account will delete the Xbox account from the phone presumably it will?
when I tap and hold, the only option I get is "sync"
You will probably have to do a factory reset. That first Live ID setup is critical.
Have you tried putting fake credentials in the second (real) account and then putting the credentials for the real account into the second account? From there, you should be able to delete the second account. I would think that the phone details are locked to an account, not a specific instance of an account, although I've never had to test this.