I'm usually the last person to talk anyone out of driving, but in this case are you sure you wouldn't be better flying south and renting a car for 8 or 9 days ? To include the coast road between SF and LA you have about 8.5 days on the road, without any possible weather disruption considered and 7 month old twins to cater for. You will need to stop more regular and for longer each time they need a feed or nappy changing and general parenting if they are unhappy. If one [or both] of them has a bad night and keep you awake, you could end up exhausted the next day. "As fast as possible" really takes on a new meaning with babies to consider. ;-)

The trip is possible if you want to spend the most part driving over Christmas, but if you are planning on a couple of days in SF and LA to do shopping and sight seeing then you need to reconsider in my opinion.