With excel formulas you cannot really move data. Your represent it in other cells using formulas. So, to that end you cannot move rows from a sheet to another by using a formula. But, you can identify what cells to select using autofilter, and cut and paste them into a new worksheet.
So, for the formula you want to use, you would put the reference date in a cell on the top row of an unused column adjacent to your data.
the twos weeks prior formula would be something like this, assuming the record date is in cell B2, and the date check column is column C. The reference date is in cell C1. You would enter the following formula in cell C2 and copy down:
This will give you a TRUE/FALSE result Then Filter.
PS. YOu do not show what version of excel you use. Sometimes solutions are non existent or more difficult in earlier versions and it helps the forum help you. Using the xl2bb add in (link below) also allows you (and responders) to post mini workbooks that can be pasted into their own machines.