Hi guys,
The short answer is, currently you need to 'download' everything to maintain synchronised libraries. But of course with USB flash sticks and local networking you don't have to download everything again, you can simply transfer the files from one computer to the other, which will be much faster.
As for 2010BEBES' question, each license key you own allows up to two activations; in other words, you can have one LR at mum's and one at either dad's or grandma's, but not all three.
Sorry for the inconvenience!
Cheers,
shuki