Just rerun the slingbox setup in Vegas once you've installed the new router. Check to make sure you've got the port forwarding done correctly,
check your slingbox status to see if there are any warning signs that show up with remote viewing by signing into your account here
If everything looks good on the slingbox end, you should be good to go on the slingcatcher side. I would run the slingplayer on your P.C, do an alt.shift.i on the keyboard and just verify that you have a TCP stream running so you won't have any issue with connecting to your slingcatcher when you get back to Mexico.