Yeah, lots of backtracking
And you need to add the time to get into the parks. Driving congestion, trying to find a parking place, etc. add up, too. So any time you can save on the road itself, will be appreciated in the end. And staying at campgrounds within the national parks usually put you in more beautiful settings, too.
You will want to get a National Parks Pass. It will save you money with all the parks you are visiting.
Out of curiousity, I plugged your route into GoogleMaps. Here it is. Then I redid your route to make it more efficient (but still visually stupendous). The new route saves you 347 miles. To be fair, over five weeks, that 347 miles isn't going to matter a lot. But it does give you an extra day someplace to lay-over and relax from the road. You all might need a day for that. Even if you do nothing but spend an extra day at a campground someplace and let the kids play in the pool while you and your husband take turns napping.
I did leave out the coastal drive but, since that part of your route probably wouldn't change, it doesn't impact the miles saved, although your totals miles for each route would be more.
Buy a set of cable chains and keep them in the car
I carry a set of cable chains 365 days a year -- they don't take much room and they work very well for all but off-road conditions.
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Also, will anyone read this as it is in my original thread relating to San Fran to LA???!!
What does this mean?
Mark