Actually, I was on the phone for about 6 hours last night with Apple Genius- we deleted history, deleted preferences, went through everything imaginable - (put it in the trash, restarted, but essentially saved everything just to test- and NOTHING worked). He couldn't figure out what was going on. So we made a log from my computer and it's going to the Apple Engineers to try to see what's happening.
but just for your information- I can of course get to a url for youtube.com - but when I click "login" the page would just refreshes itself. Nothing changed- groundhog day, over again.... I CAN login to youtube on Firefox, but there was something going on with only that page, and Safari.
He told me from everything I tried there's some mysterious thing going on that the engineers would have to evaluate.
I guess I have to click that the issue has been solved, although it hasn't because nice people are sincerely trying to help- but the Apple Genius ALSO told me that there is no way to delete part of the history - like searching just for "youtube" specifically, and trying to delete all of those.... It can't be done right now. I think it's a mistake that they didn't allow for that, but alas, that is the situation.
Again, thanks for trying!