It doesn't matter whether you put in two applications or you and your wife each put in one -- your chances are the same. (It is the Half Dome permits that are rejected if someone applies more than once.)
If your two applications both are successful, you will be charged twice, and it is non-refundable. Your credit card info is collected with your applications to use immediately once your lottery slot is successful. You won't get a chance to cancel before the charge is made.
If people were allowed to cancel with a refund, many would be putting in a lot more applications.
