You won't be at home with your family; you'll be at Disneyland with them. Guess lots of others think like you.
We have often been during Thanksgiving week, but we always go home on the Saturday, so I can't be a lot of help for your particular days. I can tell you that Wednesday before Thanksgiving is usually the worst of the week. Friday after Thanksgiving is pretty busy, usually feels busier than Thanksgiving Day itself. From what I've heard, the crowds start to decrease some on Sunday and then get pretty tolerable on the Monday and Tuesday after Thanksgiving, so you should get both some crowded and uncrowded days.
Late Friday night after Thanksgiving in 2011 was busy but not terrible. Saturday was fine. Sunday, I thought was light; Sunday night gets to be bordering on very light. (I got a Space Mountain Fastpass at 9:50 PM, if I recall correctly. When I've gone during busy summer times the FPs are all gone by mid-afternoon, so in 2011 the parks were nowhere near capacity, IMO.)
That said, 2012 could very well be very different. Cars Land is a huge factor, and also, it seems like every few days, someone posts saying they're going after Thanksgiving and asking how it is. So maybe it will be insane this year? But in 2011 it really wasn't awful.