The sling setup for the new router will have to be done at the slingbox location, but your only option could be, if your brother in law has a computer at the slingbox location, is to get him to install the free logmein remote controlling software on to his computer. You use your computer to take over his computer, sign in to your sling account. Re-run the setup with the new router and you should be good to go.
I've got a computer setup this way at my slingbox location in case I need remote access. This helps when you don't have a tech savvy family.
Send the download link for him to setup a free account, Once installed and running on his end, you'll just need a plugin added to your browser. Sign in to the account and take over his computer letting you access the slingbox and the new router.
That's about your only option unless you can talk him through the setup over the phone or use I.M.