Yes, you can. I use it at both my primary and vacation residence through multiple devices (iPad, Panny LCD TV, PC).
As long as your grandkids have the right equipment available, you'll be fine (i.e. don't expect a 10 year old PC to provide excellent results).
^ Does Amazon require you to register the device you use, or can you simply sign in and start watching?
Dazed and confused over high tech.
Sigh...Concrap. The Internet Overlord Cometh
They're not com-tastic!
You have to register your device, you can check your devices at Amazon Instant Video Settings and Devices under your account info.