I grew up on the coast in N CA and have driven by Crater Lake a bunch in the winter time. You can tent camp in the Redwoods that time of year, just be prepared for rain and lots of it. Temps will be in the 40/50's probably, might get down in the 30's at night. You might luck out and get a week of good weather that time of year but don't count on it. Be prepared for everything to be damp, constantly, in a tent. Wear layers and have some rain gear. A lot of the camp grounds and some attractions will be closed too that time of year, either for seasonal closures or because of weather related issues. When you get closer to going and have a route figured out pm me for some good spots in Humboldt County and north.
I wouldn't tent camp in Crater Lake that time of year unless you had some training and gear for it. Snowfall is measured in feet, not inches. I would have gear rated for sub zero temps. You can also only access the southern entrance then too. The highway along the Umpqua between Crater Lake and Roseburg OR is awesome, so is the road between Gold Point and Crater Lake. Both roads have lots of campgrounds along them too, not sure if they are all open that time of year. Both Roseburg and Medford are on I5 and have quite a few inexpensive hotels.
The time of year you are coming out is the off season so you won't have to fight crowds but alot of stuff will be closed. You will also run into snow, most places you will go will involve crossing mountain ranges where you could run into snow and ice on the road.
Pack rain boots for the little ones. Lots of puddles to play in.