Sending a second reminder to a professor about LORs, after the first reminder
A week since your first reminder is somewhat on the short side - personally I would wait a couple more days (maybe two weeks since the last email) to send another email. 

A week before the deadline is a good point of time to send a reminder. There is no need to state that this is a second (or nth) reminder. A short email, roughly of the form 'thanks again for agreeing to write a recommendation letter for me. I just wanted to quickly remind you that the deadlines are one week away. Please let me know if you need any more information from me. Thanks again for all your help, etc.' is sufficient.