I suspect that when you applied the update to your SlingPlayer software, it lost track of the location of your Slingblx, so you could no longer log in from the Slingplayer software to the Slingbox. One solution to this would be to get a "permanent", static IP address assigned to your Slingbox by your router, so that the address of the Slingbox will always be the same, regardless of whether your router reboots or you update your SlingPlayer software.
So my suggestion would be to check the users manual of new router for instructions on how to assign a static IP address to devices attached to it (note that this is different from assigning a static IP address to the router iteself, which you do not want to do), copy down the Media Access Control (MAC) ID for your Slingbox (probably printed on a sticker on the bottom of the Slingbox), then program your router to assign a static IP address to the device with the MAC ID of your Slingbox.
Then program your router to forward port 5001 to the static IP address that you assigned to your Slingbox. Unplug the power on the Slingbox, unplug the power on your router; wait 20 seconds, power up the router; when it's lights settle down, power up the Slingbox. Then see if the Slingbox's lights settle down and whether you can communicate with the Slingbox once again within your home. Then also ask your daughter to see if she can view the Slingbox from Italy.
And when you then log in to your account on www.slingbox.com and click the Support tab, you should see the name and serial number of your Slingbox and both the IP address of your router and this local address that you programmed your router to assign to the Slingbox. Plus an indication that Internet viewing is good to go.