Ok lookerup, good problem solving their :-), both of the points you raise are good ones.
So, potentially, the website in question, youtube, may be experiencing a lot of traffic ( many users connected stressing out their servers! ), while other sites are fine. This is common over the weekend when many more people ( school kids and working mums and dads ) are using the internet, something to bear in mind!
Your assessment of your other PC's being connected to your home network is also correct, you suffer from the same problem internally ( 3 or more PC's sharing your home bandwidth ( contention rate again! ) which can and will slow down your own connection speed to internet!
Excellent summary and better understanding of problem. Not much you can do about the server side of things, many more people connecting to youtube, just have to live with that. :-(
On your home network, you could always turn of net connection for other PC's ( kids won't be happy ) and there-by guarantee you get all local bandwidth and suffer no local contention :-) hehehehe, not elegant but a definite solution.
Hope this all helps in any small way. good luck :-0