This happens when your CPU is "overloaded" and works flat out 100%(might not show as 100% in task manager, lot of other things can be a factor). This is what is causing your youtube videos to freeze up as well as they need CPU time as well.
What you could possible do if you have a quadcore is to set affinity(rightclick tasks in the taskmanager) to all but one of the cores to Minecraft and then the core that is left to the flashplayer(I think that is what runs your Youtube videos). You get best performance if you assign physical cores and not hyperthreads(generally 0,2,4,6 are physical cores). That might help. But you might also experience worse performance in both. /shrug
I only have a 3 core, I've set it to 2/3 running MC - hopefully this fixes; if not, I'll edit this "post" to update...