What if you moved back into your rental property and started using it as your primary residence? Wouldn't you be able to deduct the mortgage interest for the portion of time that you used it as a primary residence on Itemized Deductions (Schedule A)? If so, would I re-enter the mortgage interest from the 1098 again into the Itemized Deductions section or do I assume that Turbo Tax is automatically doing that?

If a property is used both as a personal residence and as a rental during the tax year, you must pro-rate the expenses accordingly.  Only the portion attributable to the rental period goes to Schedule E.  Note that hazard insurance premiums are deductible for a rental, but not for your personal residence.