Desktop payroll (unless you have something different) can be run without any internet connection other than for updates and transmitting direct deposit information. For anything requiring internet connectivity to Intuit you can use any reliable and secure internet connection. I would never use the free wifi at Starbucks or other public wifi to access my Intuit account (or any other password enabled account for that matter). The family member's internet might be slower than your office but if it has a wpa password protected login you should be fine.
If you have a smartphone with hotspot capabilities you might consider using it instead, as it will probably be 5 times faster than any home DSL connection (I know mine is)
One option I have when I travel is that there is always someone back at the office with access to a printer, the checks and who is authorized to sign. I run payroll, print checks to PDF (using free BullZip Printer as my preference) saving the PDF in the process. Then I email the PDF to the associate, who then prints and delivers the checks. This works with all other bill pay and expenditure checks as well and there is no discernible difference than if I was back in the office
