If you're using the transferspreadsheet function in Access, you will not be able to export data to an existing spreadsheet. Just one of the limitations of the export parameter of this command.
What you could do is, in your Excel spreadsheet, use the Get External data function. From the toolbar: |Data|Get External Data|New Database Query|. Its a wizard that creates a query that will let you bring in data from any table in any Access db. It does work very well. And, once the 'import data query' is saved, you can execute it with a macro from Excel, if you want. Might take a little bit of practice though, to get the data you want and to know where everything is saved. But I have had good luck with importing data this way. Of course, your users will have to get into Excel to start this process. If you have to have this whole process start in Access, you probably would have to have Access open the Spreadsheet then on the WorkBook_Open event you could execute the macro to run your get data query.
Hope this helps. Good luck.