Curt, Disneyland is south of LAX, and the closure is north of LAX. If your family will be going from LAX to Disneyland on that weekend, they should be OK (although delays along that stretch are pretty common anyway). If they are planning to go north of LAX, especially on the 405 freeway, they're probably going to run into heavy delays.
The people who will be most affected will be those who are trying to travel on the 405 from the San Fernando Valley into the Los Angeles Basin, and vice versa. I drive on that stretch of road - the Sepulveda pass - nearly every day at work (sometimes multiple times in a day), but fortunately we're not planning to be working that weekend. That road is not for the faint of heart on a normal day.
I've gotten to the point where it doesn't bother me at all. Traffic's not nearly as bad when you're getting paid hourly to sit in it.
I've also gotten accustomed to driving at 75 in the car pool lane with the Jersey wall 2' from my driver's door. (We have a lot of "zero clearance" lanes with absolutely no shoulder.)
It's interesting that Glenn hasn't heard much about it. Granted, he's in the next county over, but on this side of town, it's about the only thing on the news. Every permanent and portable electronic message board on the 405, 101, 5, 118, 105, and 110 freeways I've seen for the past 3 weeks has been warning people about the closure. Last Thursday as we were driving over the Sepulveda Pass for the third time that day, we passed by what had to have been the 900th such sign we'd seen that day. In a surprised voice, I said to Perry "Did you hear they're closing the 405? When did they decide to do this?"